| 1 | """Class Domain - 1D domains for finite-volume computations of |
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| 2 | the shallow water wave equation |
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| 3 | |
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| 4 | |
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| 5 | Copyright 2004 |
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| 6 | Ole Nielsen, Stephen Roberts, Duncan Gray, Christopher Zoppou |
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| 7 | Geoscience Australia |
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| 8 | """ |
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| 9 | from generic_boundary_conditions import * |
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| 10 | #from coordinate_transforms.geo_reference import Geo_reference |
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| 11 | |
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| 12 | class Domain: |
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| 13 | |
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| 14 | def __init__(self, coordinates, boundary = None, |
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| 15 | conserved_quantities = None, other_quantities = None, |
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| 16 | tagged_elements = None): |
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| 17 | """ |
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| 18 | Build 1D elements from x coordinates |
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| 19 | """ |
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| 20 | |
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| 21 | from Numeric import array, zeros, Float, Int |
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| 22 | |
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| 23 | #Store Points |
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| 24 | self.coordinates = array(coordinates) |
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| 25 | |
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| 26 | # # if geo_reference is None: |
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| 27 | # # self. = Geo_reference() #Use defaults |
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| 28 | # # else: |
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| 29 | # # self.geo_reference = geo_reference |
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| 30 | |
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| 31 | #Register number of Elements |
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| 32 | self.number_of_elements = N = len(self.coordinates)-1 |
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| 33 | |
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| 34 | self.beta = 1.0 |
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| 35 | self.limiter = "minmod_kurganov" |
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| 36 | self.wet_nodes = zeros((N,2), Int) # should this be here |
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| 37 | |
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| 38 | #Allocate space for neighbour and boundary structures |
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| 39 | self.neighbours = zeros((N, 2), Int) |
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| 40 | #self.neighbour_edges = zeros((N, 2), Int) |
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| 41 | self.neighbour_vertices = zeros((N, 2), Int) |
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| 42 | self.number_of_boundaries = zeros(N, Int) |
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| 43 | self.surrogate_neighbours = zeros((N, 2), Int) |
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| 44 | |
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| 45 | #Allocate space for geometric quantities |
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| 46 | self.vertices = zeros((N, 2), Float) |
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| 47 | self.centroids = zeros(N, Float) |
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| 48 | self.areas = zeros(N, Float) |
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| 49 | |
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| 50 | self.max_speed_array = zeros(N, Float) |
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| 51 | |
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| 52 | self.normals = zeros((N, 2), Float) |
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| 53 | |
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| 54 | for i in range(N): |
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| 55 | xl = self.coordinates[i] |
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| 56 | xr = self.coordinates[i+1] |
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| 57 | self.vertices[i,0] = xl |
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| 58 | self.vertices[i,1] = xr |
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| 59 | |
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| 60 | centroid = (xl+xr)/2.0 |
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| 61 | self.centroids[i] = centroid |
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| 62 | |
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| 63 | msg = 'Coordinates should be ordered, smallest to largest' |
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| 64 | assert xr>xl, msg |
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| 65 | |
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| 66 | #The normal vectors |
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| 67 | # - point outward from each edge |
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| 68 | # - are orthogonal to the edge |
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| 69 | # - have unit length |
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| 70 | # - Are enumerated by left vertex then right vertex normals |
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| 71 | |
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| 72 | nl = -1.0 |
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| 73 | nr = 1.0 |
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| 74 | self.normals[i,:] = [nl, nr] |
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| 75 | |
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| 76 | self.areas[i] = (xr-xl) |
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| 77 | |
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| 78 | # # print 'N', N |
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| 79 | # # print 'Centroid', self.centroids |
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| 80 | # # print 'Areas', self.areas |
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| 81 | # # print 'Vertex_Coordinates', self.vertices |
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| 82 | |
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| 83 | #Initialise Neighbours (-1 means that it is a boundary neighbour) |
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| 84 | self.neighbours[i, :] = [-1, -1] |
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| 85 | #Initialise edge ids of neighbours |
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| 86 | #Initialise vertex ids of neighbours |
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| 87 | #In case of boundaries this slot is not used |
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| 88 | #self.neighbour_edges[i, :] = [-1, -1] |
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| 89 | self.neighbour_vertices[i, :] = [-1, -1] |
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| 90 | |
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| 91 | self.build_vertexlist() |
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| 92 | |
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| 93 | #Build neighbour structure |
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| 94 | self.build_neighbour_structure() |
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| 95 | |
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| 96 | #Build surrogate neighbour structure |
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| 97 | self.build_surrogate_neighbour_structure() |
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| 98 | |
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| 99 | #Build boundary dictionary mapping (id, edge) to symbolic tags |
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| 100 | #Build boundary dictionary mapping (id, vertex) to symbolic tags |
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| 101 | self.build_boundary_dictionary(boundary) |
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| 102 | |
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| 103 | #Build tagged element dictionary mapping (tag) to array of elements |
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| 104 | self.build_tagged_elements_dictionary(tagged_elements) |
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| 105 | |
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| 106 | from quantity import Quantity, Conserved_quantity |
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| 107 | #from quantity_domain import Quantity, Conserved_quantity |
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| 108 | |
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| 109 | #List of quantity names entering |
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| 110 | #the conservation equations |
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| 111 | #(Must be a subset of quantities) |
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| 112 | if conserved_quantities is None: |
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| 113 | self.conserved_quantities = [] |
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| 114 | else: |
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| 115 | self.conserved_quantities = conserved_quantities |
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| 116 | |
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| 117 | if other_quantities is None: |
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| 118 | self.other_quantities = [] |
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| 119 | else: |
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| 120 | self.other_quantities = other_quantities |
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| 121 | |
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| 122 | |
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| 123 | #Build dictionary of Quantity instances keyed by quantity names |
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| 124 | self.quantities = {} |
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| 125 | |
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| 126 | #FIXME: remove later - maybe OK, though.... |
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| 127 | for name in self.conserved_quantities: |
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| 128 | self.quantities[name] = Quantity(self) |
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| 129 | for name in self.other_quantities: |
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| 130 | self.quantities[name] = Quantity(self) |
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| 131 | |
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| 132 | #Create an empty list for explicit forcing terms |
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| 133 | self.forcing_terms = [] |
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| 134 | |
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| 135 | #Defaults |
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| 136 | from config import max_smallsteps, beta_w, beta_h, epsilon, CFL |
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| 137 | self.beta_w = beta_w |
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| 138 | self.beta_h = beta_h |
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| 139 | self.epsilon = epsilon |
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| 140 | |
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| 141 | #FIXME: Maybe have separate orders for h-limiter and w-limiter? |
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| 142 | #Or maybe get rid of order altogether and use beta_w and beta_h |
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| 143 | self.default_order = 1 |
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| 144 | self.order = self.default_order |
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| 145 | |
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| 146 | self.default_time_order = 1 |
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| 147 | self.time_order = self.default_time_order |
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| 148 | |
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| 149 | self.smallsteps = 0 |
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| 150 | self.max_smallsteps = max_smallsteps |
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| 151 | self.number_of_steps = 0 |
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| 152 | self.number_of_first_order_steps = 0 |
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| 153 | self.CFL = CFL |
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| 154 | |
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| 155 | #Model time |
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| 156 | self.time = 0.0 |
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| 157 | self.finaltime = None |
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| 158 | self.min_timestep = self.max_timestep = 0.0 |
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| 159 | self.starttime = 0 #Physical starttime if any (0 is 1 Jan 1970 00:00:00) |
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| 160 | #Checkpointing and storage |
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| 161 | from config import default_datadir |
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| 162 | self.datadir = default_datadir |
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| 163 | self.filename = 'domain' |
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| 164 | self.checkpoint = False |
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| 165 | |
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| 166 | def __len__(self): |
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| 167 | return self.number_of_elements |
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| 168 | |
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| 169 | def build_vertexlist(self): |
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| 170 | """Build vertexlist index by vertex ids and for each entry (point id) |
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| 171 | build a list of (triangles, vertex_id) pairs that use the point |
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| 172 | as vertex. |
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| 173 | |
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| 174 | Preconditions: |
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| 175 | self.coordinates and self.triangles are defined |
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| 176 | |
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| 177 | Postcondition: |
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| 178 | self.vertexlist is built |
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| 179 | """ |
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| 180 | from Numeric import array |
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| 181 | |
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| 182 | vertexlist = [None]*len(self.coordinates) |
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| 183 | for i in range(self.number_of_elements): |
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| 184 | |
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| 185 | #a = self.triangles[i, 0] |
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| 186 | #b = self.triangles[i, 1] |
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| 187 | #c = self.triangles[i, 2] |
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| 188 | a = i |
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| 189 | b = i + 1 |
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| 190 | |
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| 191 | #Register the vertices v as lists of |
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| 192 | #(triangle_id, vertex_id) tuples associated with them |
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| 193 | #This is used for smoothing |
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| 194 | #for vertex_id, v in enumerate([a,b,c]): |
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| 195 | for vertex_id, v in enumerate([a,b]): |
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| 196 | if vertexlist[v] is None: |
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| 197 | vertexlist[v] = [] |
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| 198 | |
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| 199 | vertexlist[v].append( (i, vertex_id) ) |
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| 200 | |
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| 201 | self.vertexlist = vertexlist |
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| 202 | |
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| 203 | |
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| 204 | def build_neighbour_structure(self): |
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| 205 | """Update all registered triangles to point to their neighbours. |
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| 206 | |
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| 207 | Also, keep a tally of the number of boundaries for each triangle |
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| 208 | |
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| 209 | Postconditions: |
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| 210 | neighbours and neighbour_edges is populated |
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| 211 | neighbours and neighbour_vertices is populated |
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| 212 | number_of_boundaries integer array is defined. |
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| 213 | """ |
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| 214 | |
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| 215 | #Step 1: |
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| 216 | #Build dictionary mapping from segments (2-tuple of points) |
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| 217 | #to left hand side edge (facing neighbouring triangle) |
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| 218 | |
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| 219 | N = self.number_of_elements |
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| 220 | neighbourdict = {} |
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| 221 | #l_edge = 0 |
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| 222 | #r_edge = 1 |
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| 223 | l_vertex = 0 |
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| 224 | r_vertex = 1 |
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| 225 | for i in range(N): |
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| 226 | |
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| 227 | #Register all segments as keys mapping to current triangle |
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| 228 | #and segment id |
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| 229 | #a = self.triangles[i, 0] |
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| 230 | #b = self.triangles[i, 1] |
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| 231 | #c = self.triangles[i, 2] |
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| 232 | a = self.vertices[i,0] |
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| 233 | b = self.vertices[i,1] |
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| 234 | |
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| 235 | """ |
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| 236 | if neighbourdict.has_key((a,b)): |
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| 237 | msg = "Edge 2 of triangle %d is duplicating edge %d of triangle %d.\n" %(i,neighbourdict[a,b][1],neighbourdict[a,b][0]) |
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| 238 | raise msg |
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| 239 | if neighbourdict.has_key((b,c)): |
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| 240 | msg = "Edge 0 of triangle %d is duplicating edge %d of triangle %d.\n" %(i,neighbourdict[b,c][1],neighbourdict[b,c][0]) |
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| 241 | raise msg |
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| 242 | if neighbourdict.has_key((c,a)): |
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| 243 | msg = "Edge 1 of triangle %d is duplicating edge %d of triangle %d.\n" %(i,neighbourdict[c,a][1],neighbourdict[c,a][0]) |
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| 244 | raise msg |
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| 245 | """ |
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| 246 | #neighbourdict[a,b] = (i, 2) #(id, edge) |
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| 247 | #neighbourdict[b,c] = (i, 0) #(id, edge) |
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| 248 | #neighbourdict[c,a] = (i, 1) #(id, edge) |
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| 249 | #neighbourdict[a,b] = (i, 1) #(id, edge) |
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| 250 | #neighbourdict[b,a] = (i, 0) #(id, edge) |
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| 251 | #neighbourdict[a,l_edge] = (i, 0) #(id, edge) |
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| 252 | #neighbourdict[b,r_edge] = (i, 1) #(id, edge) |
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| 253 | neighbourdict[a,l_vertex] = (i, 0) #(id, vertex) |
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| 254 | neighbourdict[b,r_vertex] = (i, 1) #(id, vertex) |
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| 255 | |
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| 256 | |
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| 257 | #Step 2: |
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| 258 | #Go through triangles again, but this time |
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| 259 | #reverse direction of segments and lookup neighbours. |
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| 260 | for i in range(N): |
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| 261 | #a = self.triangles[i, 0] |
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| 262 | #b = self.triangles[i, 1] |
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| 263 | #c = self.triangles[i, 2] |
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| 264 | |
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| 265 | a = self.vertices[i,0] |
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| 266 | b = self.vertices[i,1] |
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| 267 | |
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| 268 | #self.number_of_boundaries[i] = 3 |
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| 269 | self.number_of_boundaries[i] = 2 |
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| 270 | #if neighbourdict.has_key((b,l_edge)): |
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| 271 | if neighbourdict.has_key((b,l_vertex)): |
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| 272 | #self.neighbours[i, 1] = neighbourdict[b,l_edge][0] |
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| 273 | #self.neighbour_edges[i, 1] = neighbourdict[b,l_edge][1] |
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| 274 | self.neighbours[i, 1] = neighbourdict[b,l_vertex][0] |
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| 275 | self.neighbour_vertices[i, 1] = neighbourdict[b,l_vertex][1] |
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| 276 | self.number_of_boundaries[i] -= 1 |
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| 277 | |
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| 278 | #if neighbourdict.has_key((a,r_edge)): |
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| 279 | if neighbourdict.has_key((a,r_vertex)): |
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| 280 | #self.neighbours[i, 0] = neighbourdict[a,r_edge][0] |
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| 281 | #self.neighbour_edges[i, 0] = neighbourdict[a,r_edge][1] |
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| 282 | self.neighbours[i, 0] = neighbourdict[a,r_vertex][0] |
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| 283 | self.neighbour_vertices[i, 0] = neighbourdict[a,r_vertex][1] |
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| 284 | self.number_of_boundaries[i] -= 1 |
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| 285 | |
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| 286 | #if neighbourdict.has_key((b,a)): |
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| 287 | # self.neighbours[i, 1] = neighbourdict[b,a][0] |
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| 288 | # self.neighbour_edges[i, 1] = neighbourdict[b,a][1] |
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| 289 | # self.number_of_boundaries[i] -= 1 |
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| 290 | |
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| 291 | #if neighbourdict.has_key((c,b)): |
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| 292 | # self.neighbours[i, 0] = neighbourdict[c,b][0] |
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| 293 | # self.neighbour_edges[i, 0] = neighbourdict[c,b][1] |
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| 294 | # self.number_of_boundaries[i] -= 1 |
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| 295 | |
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| 296 | #if neighbourdict.has_key((a,b)): |
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| 297 | # self.neighbours[i, 0] = neighbourdict[a,b][0] |
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| 298 | # self.neighbour_edges[i, 0] = neighbourdict[a,b][1] |
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| 299 | # self.number_of_boundaries[i] -= 1 |
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| 300 | |
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| 301 | def build_surrogate_neighbour_structure(self): |
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| 302 | """Build structure where each triangle edge points to its neighbours |
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| 303 | if they exist. Otherwise point to the triangle itself. |
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| 304 | |
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| 305 | The surrogate neighbour structure is useful for computing gradients |
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| 306 | based on centroid values of neighbours. |
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| 307 | |
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| 308 | Precondition: Neighbour structure is defined |
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| 309 | Postcondition: |
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| 310 | Surrogate neighbour structure is defined: |
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| 311 | surrogate_neighbours: i0, i1, i2 where all i_k >= 0 point to |
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| 312 | triangles. |
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| 313 | |
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| 314 | """ |
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| 315 | |
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| 316 | N = self.number_of_elements |
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| 317 | for i in range(N): |
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| 318 | #Find all neighbouring volumes that are not boundaries |
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| 319 | #for k in range(3): |
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| 320 | for k in range(2): |
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| 321 | if self.neighbours[i, k] < 0: |
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| 322 | self.surrogate_neighbours[i, k] = i #Point this triangle |
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| 323 | else: |
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| 324 | self.surrogate_neighbours[i, k] = self.neighbours[i, k] |
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| 325 | |
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| 326 | def build_boundary_dictionary(self, boundary = None): |
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| 327 | """Build or check the dictionary of boundary tags. |
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| 328 | self.boundary is a dictionary of tags, |
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| 329 | keyed by volume id and edge: |
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| 330 | { (id, edge): tag, ... } |
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| 331 | |
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| 332 | Postconditions: |
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| 333 | self.boundary is defined. |
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| 334 | """ |
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| 335 | |
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| 336 | from config import default_boundary_tag |
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| 337 | |
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| 338 | if boundary is None: |
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| 339 | boundary = {} |
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| 340 | for vol_id in range(self.number_of_elements): |
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| 341 | #for edge_id in range(0, 3): |
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| 342 | #for edge_id in range(0, 2): |
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| 343 | for vertex_id in range(0, 2): |
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| 344 | #if self.neighbours[vol_id, edge_id] < 0: |
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| 345 | if self.neighbours[vol_id, vertex_id] < 0: |
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| 346 | #boundary[(vol_id, edge_id)] = default_boundary_tag |
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| 347 | boundary[(vol_id, vertex_id)] = default_boundary_tag |
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| 348 | else: |
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| 349 | #Check that all keys in given boundary exist |
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| 350 | #for vol_id, edge_id in boundary.keys(): |
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| 351 | for vol_id, vertex_id in boundary.keys(): |
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| 352 | #msg = 'Segment (%d, %d) does not exist' %(vol_id, edge_id) |
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| 353 | msg = 'Segment (%d, %d) does not exist' %(vol_id, vertex_id) |
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| 354 | a, b = self.neighbours.shape |
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| 355 | #assert vol_id < a and edge_id < b, msg |
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| 356 | assert vol_id < a and vertex_id < b, msg |
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| 357 | |
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| 358 | #FIXME: This assert violates internal boundaries (delete it) |
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| 359 | #msg = 'Segment (%d, %d) is not a boundary' %(vol_id, edge_id) |
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| 360 | #assert self.neighbours[vol_id, edge_id] < 0, msg |
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| 361 | |
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| 362 | #Check that all boundary segments are assigned a tag |
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| 363 | for vol_id in range(self.number_of_elements): |
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| 364 | #for edge_id in range(0, 3): |
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| 365 | #for edge_id in range(0, 2): |
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| 366 | for vertex_id in range(0, 2): |
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| 367 | #if self.neighbours[vol_id, edge_id] < 0: |
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| 368 | if self.neighbours[vol_id, vertex_id] < 0: |
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| 369 | #if not boundary.has_key( (vol_id, edge_id) ): |
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| 370 | if not boundary.has_key( (vol_id, vertex_id) ): |
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| 371 | msg = 'WARNING: Given boundary does not contain ' |
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| 372 | #msg += 'tags for edge (%d, %d). '\ |
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| 373 | # %(vol_id, edge_id) |
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| 374 | msg += 'tags for vertex (%d, %d). '\ |
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| 375 | %(vol_id, vertex_id) |
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| 376 | msg += 'Assigning default tag (%s).'\ |
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| 377 | %default_boundary_tag |
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| 378 | |
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| 379 | #FIXME: Print only as per verbosity |
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| 380 | #print msg |
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| 381 | |
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| 382 | #FIXME: Make this situation an error in the future |
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| 383 | #and make another function which will |
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| 384 | #enable default boundary-tags where |
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| 385 | #tags a not specified |
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| 386 | #boundary[ (vol_id, edge_id) ] =\ |
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| 387 | boundary[ (vol_id, vertex_id) ] =\ |
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| 388 | default_boundary_tag |
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| 389 | |
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| 390 | |
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| 391 | |
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| 392 | self.boundary = boundary |
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| 393 | |
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| 394 | def build_tagged_elements_dictionary(self, tagged_elements = None): |
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| 395 | """Build the dictionary of element tags. |
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| 396 | self.tagged_elements is a dictionary of element arrays, |
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| 397 | keyed by tag: |
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| 398 | { (tag): [e1, e2, e3..] } |
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| 399 | |
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| 400 | Postconditions: |
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| 401 | self.element_tag is defined |
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| 402 | """ |
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| 403 | from Numeric import array, Int |
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| 404 | |
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| 405 | if tagged_elements is None: |
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| 406 | tagged_elements = {} |
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| 407 | else: |
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| 408 | #Check that all keys in given boundary exist |
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| 409 | for tag in tagged_elements.keys(): |
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| 410 | tagged_elements[tag] = array(tagged_elements[tag]).astype(Int) |
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| 411 | |
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| 412 | msg = 'Not all elements exist. ' |
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| 413 | assert max(tagged_elements[tag]) < self.number_of_elements, msg |
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| 414 | #print "tagged_elements", tagged_elements |
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| 415 | self.tagged_elements = tagged_elements |
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| 416 | |
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| 417 | def get_boundary_tags(self): |
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| 418 | """Return list of available boundary tags |
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| 419 | """ |
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| 420 | |
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| 421 | tags = {} |
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| 422 | for v in self.boundary.values(): |
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| 423 | tags[v] = 1 |
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| 424 | |
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| 425 | return tags.keys() |
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| 426 | |
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| 427 | def get_vertex_coordinates(self, obj = False): |
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| 428 | """Return all vertex coordinates. |
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| 429 | Return all vertex coordinates for all triangles as an Nx6 array |
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| 430 | (ordered as x0, y0, x1, y1, x2, y2 for each triangle) |
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| 431 | |
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| 432 | if obj is True, the x/y pairs are returned in a 3*N x 2 array. |
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| 433 | FIXME, we might make that the default. |
|---|
| 434 | FIXME Maybe use keyword: continuous = False for this condition? |
|---|
| 435 | |
|---|
| 436 | |
|---|
| 437 | """ |
|---|
| 438 | |
|---|
| 439 | if obj is True: |
|---|
| 440 | from Numeric import concatenate, reshape |
|---|
| 441 | #V = self.vertex_coordinates |
|---|
| 442 | V = self.vertices |
|---|
| 443 | #return concatenate( (V[:,0:2], V[:,2:4], V[:,4:6]), axis=0) |
|---|
| 444 | |
|---|
| 445 | N = V.shape[0] |
|---|
| 446 | #return reshape(V, (3*N, 2)) |
|---|
| 447 | return reshape(V, (N, 2)) |
|---|
| 448 | else: |
|---|
| 449 | #return self.vertex_coordinates |
|---|
| 450 | return self.vertices |
|---|
| 451 | |
|---|
| 452 | def get_conserved_quantities(self, vol_id, vertex=None):#, edge=None): |
|---|
| 453 | """Get conserved quantities at volume vol_id |
|---|
| 454 | |
|---|
| 455 | If vertex is specified use it as index for vertex values |
|---|
| 456 | If edge is specified use it as index for edge values |
|---|
| 457 | If neither are specified use centroid values |
|---|
| 458 | If both are specified an exeception is raised |
|---|
| 459 | |
|---|
| 460 | Return value: Vector of length == number_of_conserved quantities |
|---|
| 461 | |
|---|
| 462 | """ |
|---|
| 463 | |
|---|
| 464 | from Numeric import zeros, Float |
|---|
| 465 | |
|---|
| 466 | #if not (vertex is None):# or edge is None): |
|---|
| 467 | # msg = 'Values for both vertex and edge was specified.' |
|---|
| 468 | # msg += 'Only one (or none) is allowed.' |
|---|
| 469 | # raise msg |
|---|
| 470 | |
|---|
| 471 | q = zeros( len(self.conserved_quantities), Float) |
|---|
| 472 | |
|---|
| 473 | for i, name in enumerate(self.conserved_quantities): |
|---|
| 474 | Q = self.quantities[name] |
|---|
| 475 | if vertex is not None: |
|---|
| 476 | q[i] = Q.vertex_values[vol_id, vertex] |
|---|
| 477 | #elif edge is not None: |
|---|
| 478 | # q[i] = Q.edge_values[vol_id, edge] |
|---|
| 479 | else: |
|---|
| 480 | q[i] = Q.centroid_values[vol_id] |
|---|
| 481 | |
|---|
| 482 | return q |
|---|
| 483 | |
|---|
| 484 | |
|---|
| 485 | def get_centroids(self): |
|---|
| 486 | """Return all coordinates of centroids |
|---|
| 487 | Return x coordinate of centroid for each element as a N array |
|---|
| 488 | """ |
|---|
| 489 | |
|---|
| 490 | return self.centroids |
|---|
| 491 | |
|---|
| 492 | def get_vertices(self): |
|---|
| 493 | """Return all coordinates of centroids |
|---|
| 494 | Return x coordinate of centroid for each element as a N array |
|---|
| 495 | """ |
|---|
| 496 | |
|---|
| 497 | return self.vertices |
|---|
| 498 | |
|---|
| 499 | def get_coordinate(self, elem_id, vertex=None): |
|---|
| 500 | """Return coordinate of centroid, |
|---|
| 501 | or left or right vertex. |
|---|
| 502 | Left vertex (vertex=0). Right vertex (vertex=1) |
|---|
| 503 | """ |
|---|
| 504 | |
|---|
| 505 | if vertex is None: |
|---|
| 506 | return self.centroids[elem_id] |
|---|
| 507 | else: |
|---|
| 508 | return self.vertices[elem_id,vertex] |
|---|
| 509 | |
|---|
| 510 | def get_area(self, elem_id): |
|---|
| 511 | """Return area of element id |
|---|
| 512 | """ |
|---|
| 513 | |
|---|
| 514 | return self.areas[elem_id] |
|---|
| 515 | |
|---|
| 516 | def get_quantity(self, name, location='vertices', indices = None): |
|---|
| 517 | """Get values for named quantity |
|---|
| 518 | |
|---|
| 519 | name: Name of quantity |
|---|
| 520 | |
|---|
| 521 | In case of location == 'centroids' the dimension values must |
|---|
| 522 | be a list of a Numerical array of length N, N being the number |
|---|
| 523 | of elements. Otherwise it must be of dimension Nx3. |
|---|
| 524 | |
|---|
| 525 | Indices is the set of element ids that the operation applies to. |
|---|
| 526 | |
|---|
| 527 | The values will be stored in elements following their |
|---|
| 528 | internal ordering. |
|---|
| 529 | """ |
|---|
| 530 | |
|---|
| 531 | return self.quantities[name].get_values( location, indices = indices) |
|---|
| 532 | |
|---|
| 533 | def get_centroid_coordinates(self): |
|---|
| 534 | """Return all centroid coordinates. |
|---|
| 535 | Return all centroid coordinates for all triangles as an Nx2 array |
|---|
| 536 | (ordered as x0, y0 for each triangle) |
|---|
| 537 | """ |
|---|
| 538 | return self.centroids |
|---|
| 539 | |
|---|
| 540 | def set_quantity(self, name, *args, **kwargs): |
|---|
| 541 | """Set values for named quantity |
|---|
| 542 | |
|---|
| 543 | |
|---|
| 544 | One keyword argument is documented here: |
|---|
| 545 | expression = None, # Arbitrary expression |
|---|
| 546 | |
|---|
| 547 | expression: |
|---|
| 548 | Arbitrary expression involving quantity names |
|---|
| 549 | |
|---|
| 550 | See Quantity.set_values for further documentation. |
|---|
| 551 | """ |
|---|
| 552 | |
|---|
| 553 | #FIXME (Ole): Allow new quantities here |
|---|
| 554 | #from quantity import Quantity, Conserved_quantity |
|---|
| 555 | #Create appropriate quantity object |
|---|
| 556 | # #if name in self.conserved_quantities: |
|---|
| 557 | # # self.quantities[name] = Conserved_quantity(self) |
|---|
| 558 | # #else: |
|---|
| 559 | # # self.quantities[name] = Quantity(self) |
|---|
| 560 | |
|---|
| 561 | |
|---|
| 562 | #Do the expression stuff |
|---|
| 563 | if kwargs.has_key('expression'): |
|---|
| 564 | expression = kwargs['expression'] |
|---|
| 565 | del kwargs['expression'] |
|---|
| 566 | |
|---|
| 567 | Q = self.create_quantity_from_expression(expression) |
|---|
| 568 | kwargs['quantity'] = Q |
|---|
| 569 | |
|---|
| 570 | #Assign values |
|---|
| 571 | self.quantities[name].set_values(*args, **kwargs) |
|---|
| 572 | |
|---|
| 573 | def set_boundary(self, boundary_map): |
|---|
| 574 | """Associate boundary objects with tagged boundary segments. |
|---|
| 575 | |
|---|
| 576 | Input boundary_map is a dictionary of boundary objects keyed |
|---|
| 577 | by symbolic tags to matched against tags in the internal dictionary |
|---|
| 578 | self.boundary. |
|---|
| 579 | |
|---|
| 580 | As result one pointer to a boundary object is stored for each vertex |
|---|
| 581 | in the list self.boundary_objects. |
|---|
| 582 | More entries may point to the same boundary object |
|---|
| 583 | |
|---|
| 584 | Schematically the mapping is from two dictionaries to one list |
|---|
| 585 | where the index is used as pointer to the boundary_values arrays |
|---|
| 586 | within each quantity. |
|---|
| 587 | |
|---|
| 588 | self.boundary: (vol_id, edge_id): tag |
|---|
| 589 | boundary_map (input): tag: boundary_object |
|---|
| 590 | ---------------------------------------------- |
|---|
| 591 | self.boundary_objects: ((vol_id, edge_id), boundary_object) |
|---|
| 592 | |
|---|
| 593 | |
|---|
| 594 | Pre-condition: |
|---|
| 595 | self.boundary has been built. |
|---|
| 596 | |
|---|
| 597 | Post-condition: |
|---|
| 598 | self.boundary_objects is built |
|---|
| 599 | |
|---|
| 600 | If a tag from the domain doesn't appear in the input dictionary an |
|---|
| 601 | exception is raised. |
|---|
| 602 | However, if a tag is not used to the domain, no error is thrown. |
|---|
| 603 | FIXME: This would lead to implementation of a |
|---|
| 604 | default boundary condition |
|---|
| 605 | |
|---|
| 606 | Note: If a segment is listed in the boundary dictionary and if it is |
|---|
| 607 | not None, it *will* become a boundary - |
|---|
| 608 | even if there is a neighbouring triangle. |
|---|
| 609 | This would be the case for internal boundaries |
|---|
| 610 | |
|---|
| 611 | Boundary objects that are None will be skipped. |
|---|
| 612 | |
|---|
| 613 | FIXME: If set_boundary is called multiple times and if Boundary |
|---|
| 614 | object is changed into None, the neighbour structure will not be |
|---|
| 615 | restored!!! |
|---|
| 616 | """ |
|---|
| 617 | |
|---|
| 618 | self.boundary_objects = [] |
|---|
| 619 | self.boundary_map = boundary_map #Store for use with eg. boundary_stats. |
|---|
| 620 | |
|---|
| 621 | #FIXME: Try to remove the sorting and fix test_mesh.py |
|---|
| 622 | x = self.boundary.keys() |
|---|
| 623 | x.sort() |
|---|
| 624 | |
|---|
| 625 | #Loop through edges that lie on the boundary and associate them with |
|---|
| 626 | #callable boundary objects depending on their tags |
|---|
| 627 | #for k, (vol_id, edge_id) in enumerate(x): |
|---|
| 628 | for k, (vol_id, vertex_id) in enumerate(x): |
|---|
| 629 | #tag = self.boundary[ (vol_id, edge_id) ] |
|---|
| 630 | tag = self.boundary[ (vol_id, vertex_id) ] |
|---|
| 631 | |
|---|
| 632 | if boundary_map.has_key(tag): |
|---|
| 633 | B = boundary_map[tag] #Get callable boundary object |
|---|
| 634 | |
|---|
| 635 | if B is not None: |
|---|
| 636 | #self.boundary_objects.append( ((vol_id, edge_id), B) ) |
|---|
| 637 | #self.neighbours[vol_id, edge_id] = -len(self.boundary_objects) |
|---|
| 638 | self.boundary_objects.append( ((vol_id, vertex_id), B) ) |
|---|
| 639 | self.neighbours[vol_id, vertex_id] = -len(self.boundary_objects) |
|---|
| 640 | else: |
|---|
| 641 | pass |
|---|
| 642 | #FIXME: Check and perhaps fix neighbour structure |
|---|
| 643 | |
|---|
| 644 | else: |
|---|
| 645 | msg = 'ERROR (domain.py): Tag "%s" has not been ' %tag |
|---|
| 646 | msg += 'bound to a boundary object.\n' |
|---|
| 647 | msg += 'All boundary tags defined in domain must appear ' |
|---|
| 648 | msg += 'in the supplied dictionary.\n' |
|---|
| 649 | msg += 'The tags are: %s' %self.get_boundary_tags() |
|---|
| 650 | raise msg |
|---|
| 651 | |
|---|
| 652 | |
|---|
| 653 | |
|---|
| 654 | def check_integrity(self): |
|---|
| 655 | #Mesh.check_integrity(self) |
|---|
| 656 | |
|---|
| 657 | for quantity in self.conserved_quantities: |
|---|
| 658 | msg = 'Conserved quantities must be a subset of all quantities' |
|---|
| 659 | assert quantity in self.quantities, msg |
|---|
| 660 | |
|---|
| 661 | # #assert hasattr(self, 'boundary_objects') |
|---|
| 662 | |
|---|
| 663 | def write_time(self): |
|---|
| 664 | print self.timestepping_statistics() |
|---|
| 665 | |
|---|
| 666 | def timestepping_statistics(self): |
|---|
| 667 | """Return string with time stepping statistics for printing or logging |
|---|
| 668 | """ |
|---|
| 669 | |
|---|
| 670 | msg = '' |
|---|
| 671 | if self.min_timestep == self.max_timestep: |
|---|
| 672 | msg += 'Time = %.4f, delta t = %.8f, steps=%d (%d)'\ |
|---|
| 673 | %(self.time, self.min_timestep, self.number_of_steps, |
|---|
| 674 | self.number_of_first_order_steps) |
|---|
| 675 | elif self.min_timestep > self.max_timestep: |
|---|
| 676 | msg += 'Time = %.4f, steps=%d (%d)'\ |
|---|
| 677 | %(self.time, self.number_of_steps, |
|---|
| 678 | self.number_of_first_order_steps) |
|---|
| 679 | else: |
|---|
| 680 | msg += 'Time = %.4f, delta t in [%.8f, %.8f], steps=%d (%d)'\ |
|---|
| 681 | %(self.time, self.min_timestep, |
|---|
| 682 | self.max_timestep, self.number_of_steps, |
|---|
| 683 | self.number_of_first_order_steps) |
|---|
| 684 | |
|---|
| 685 | return msg |
|---|
| 686 | |
|---|
| 687 | def get_name(self): |
|---|
| 688 | return self.filename |
|---|
| 689 | |
|---|
| 690 | def set_name(self, name): |
|---|
| 691 | self.filename = name |
|---|
| 692 | |
|---|
| 693 | def get_datadir(self): |
|---|
| 694 | return self.datadir |
|---|
| 695 | |
|---|
| 696 | def set_datadir(self, name): |
|---|
| 697 | self.datadir = name |
|---|
| 698 | |
|---|
| 699 | |
|---|
| 700 | #-------------------------- |
|---|
| 701 | # Main components of evolve |
|---|
| 702 | #-------------------------- |
|---|
| 703 | |
|---|
| 704 | def evolve(self, |
|---|
| 705 | yieldstep = None, |
|---|
| 706 | finaltime = None, |
|---|
| 707 | duration = None, |
|---|
| 708 | skip_initial_step = False): |
|---|
| 709 | """Evolve model through time starting from self.starttime. |
|---|
| 710 | |
|---|
| 711 | |
|---|
| 712 | yieldstep: Interval between yields where results are stored, |
|---|
| 713 | statistics written and domain inspected or |
|---|
| 714 | possibly modified. If omitted the internal predefined |
|---|
| 715 | max timestep is used. |
|---|
| 716 | Internally, smaller timesteps may be taken. |
|---|
| 717 | |
|---|
| 718 | duration: Duration of simulation |
|---|
| 719 | |
|---|
| 720 | finaltime: Time where simulation should end. This is currently |
|---|
| 721 | relative time. So it's the same as duration. |
|---|
| 722 | |
|---|
| 723 | If both duration and finaltime are given an exception is thrown. |
|---|
| 724 | |
|---|
| 725 | |
|---|
| 726 | skip_initial_step: Boolean flag that decides whether the first |
|---|
| 727 | yield step is skipped or not. This is useful for example to avoid |
|---|
| 728 | duplicate steps when multiple evolve processes are dove tailed. |
|---|
| 729 | |
|---|
| 730 | |
|---|
| 731 | Evolve is implemented as a generator and is to be called as such, e.g. |
|---|
| 732 | |
|---|
| 733 | for t in domain.evolve(yieldstep, finaltime): |
|---|
| 734 | <Do something with domain and t> |
|---|
| 735 | |
|---|
| 736 | |
|---|
| 737 | All times are given in seconds |
|---|
| 738 | |
|---|
| 739 | """ |
|---|
| 740 | |
|---|
| 741 | from config import min_timestep, max_timestep, epsilon |
|---|
| 742 | |
|---|
| 743 | # FIXME: Maybe lump into a larger check prior to evolving |
|---|
| 744 | msg = 'Boundary tags must be bound to boundary objects before ' |
|---|
| 745 | msg += 'evolving system, ' |
|---|
| 746 | msg += 'e.g. using the method set_boundary.\n' |
|---|
| 747 | msg += 'This system has the boundary tags %s '\ |
|---|
| 748 | %self.get_boundary_tags() |
|---|
| 749 | assert hasattr(self, 'boundary_objects'), msg |
|---|
| 750 | |
|---|
| 751 | |
|---|
| 752 | if yieldstep is None: |
|---|
| 753 | yieldstep = max_timestep |
|---|
| 754 | else: |
|---|
| 755 | yieldstep = float(yieldstep) |
|---|
| 756 | |
|---|
| 757 | self._order_ = self.default_order |
|---|
| 758 | |
|---|
| 759 | |
|---|
| 760 | if finaltime is not None and duration is not None: |
|---|
| 761 | # print 'F', finaltime, duration |
|---|
| 762 | msg = 'Only one of finaltime and duration may be specified' |
|---|
| 763 | raise msg |
|---|
| 764 | else: |
|---|
| 765 | if finaltime is not None: |
|---|
| 766 | self.finaltime = float(finaltime) |
|---|
| 767 | if duration is not None: |
|---|
| 768 | self.finaltime = self.starttime + float(duration) |
|---|
| 769 | |
|---|
| 770 | |
|---|
| 771 | |
|---|
| 772 | N = len(self) # Number of triangles |
|---|
| 773 | self.yieldtime = 0.0 # Track time between 'yields' |
|---|
| 774 | |
|---|
| 775 | # Initialise interval of timestep sizes (for reporting only) |
|---|
| 776 | self.min_timestep = max_timestep |
|---|
| 777 | self.max_timestep = min_timestep |
|---|
| 778 | self.number_of_steps = 0 |
|---|
| 779 | self.number_of_first_order_steps = 0 |
|---|
| 780 | |
|---|
| 781 | |
|---|
| 782 | # Update ghosts |
|---|
| 783 | self.update_ghosts() |
|---|
| 784 | |
|---|
| 785 | # Initial update of vertex and edge values |
|---|
| 786 | self.distribute_to_vertices_and_edges() |
|---|
| 787 | |
|---|
| 788 | # Update extrema if necessary (for reporting) |
|---|
| 789 | self.update_extrema() |
|---|
| 790 | |
|---|
| 791 | # Initial update boundary values |
|---|
| 792 | self.update_boundary() |
|---|
| 793 | |
|---|
| 794 | # Or maybe restore from latest checkpoint |
|---|
| 795 | if self.checkpoint is True: |
|---|
| 796 | self.goto_latest_checkpoint() |
|---|
| 797 | |
|---|
| 798 | if skip_initial_step is False: |
|---|
| 799 | yield(self.time) # Yield initial values |
|---|
| 800 | |
|---|
| 801 | while True: |
|---|
| 802 | |
|---|
| 803 | # Evolve One Step, using appropriate timestepping method |
|---|
| 804 | if self.get_timestepping_method() == 'euler': |
|---|
| 805 | self.evolve_one_euler_step(yieldstep,finaltime) |
|---|
| 806 | |
|---|
| 807 | elif self.get_timestepping_method() == 'rk2': |
|---|
| 808 | self.evolve_one_rk2_step(yieldstep,finaltime) |
|---|
| 809 | |
|---|
| 810 | elif self.get_timestepping_method() == 'rk3': |
|---|
| 811 | self.evolve_one_rk3_step(yieldstep,finaltime) |
|---|
| 812 | |
|---|
| 813 | # Update extrema if necessary (for reporting) |
|---|
| 814 | self.update_extrema() |
|---|
| 815 | |
|---|
| 816 | |
|---|
| 817 | self.yieldtime += self.timestep |
|---|
| 818 | self.number_of_steps += 1 |
|---|
| 819 | if self._order_ == 1: |
|---|
| 820 | self.number_of_first_order_steps += 1 |
|---|
| 821 | |
|---|
| 822 | # Yield results |
|---|
| 823 | if finaltime is not None and self.time >= finaltime-epsilon: |
|---|
| 824 | |
|---|
| 825 | if self.time > finaltime: |
|---|
| 826 | # FIXME (Ole, 30 April 2006): Do we need this check? |
|---|
| 827 | # Probably not (Ole, 18 September 2008). Now changed to |
|---|
| 828 | # Exception |
|---|
| 829 | msg = 'WARNING (domain.py): time overshot finaltime. ' |
|---|
| 830 | msg += 'Contact Ole.Nielsen@ga.gov.au' |
|---|
| 831 | raise Exception, msg |
|---|
| 832 | |
|---|
| 833 | |
|---|
| 834 | # Yield final time and stop |
|---|
| 835 | self.time = finaltime |
|---|
| 836 | yield(self.time) |
|---|
| 837 | break |
|---|
| 838 | |
|---|
| 839 | |
|---|
| 840 | if self.yieldtime >= yieldstep: |
|---|
| 841 | # Yield (intermediate) time and allow inspection of domain |
|---|
| 842 | |
|---|
| 843 | if self.checkpoint is True: |
|---|
| 844 | self.store_checkpoint() |
|---|
| 845 | self.delete_old_checkpoints() |
|---|
| 846 | |
|---|
| 847 | # Pass control on to outer loop for more specific actions |
|---|
| 848 | yield(self.time) |
|---|
| 849 | |
|---|
| 850 | # Reinitialise |
|---|
| 851 | self.yieldtime = 0.0 |
|---|
| 852 | self.min_timestep = max_timestep |
|---|
| 853 | self.max_timestep = min_timestep |
|---|
| 854 | self.number_of_steps = 0 |
|---|
| 855 | self.number_of_first_order_steps = 0 |
|---|
| 856 | self.max_speed = zeros(N, Float) |
|---|
| 857 | |
|---|
| 858 | |
|---|
| 859 | def evolve_one_euler_step(self, yieldstep, finaltime): |
|---|
| 860 | """ |
|---|
| 861 | One Euler Time Step |
|---|
| 862 | Q^{n+1} = E(h) Q^n |
|---|
| 863 | """ |
|---|
| 864 | |
|---|
| 865 | # Compute fluxes across each element edge |
|---|
| 866 | self.compute_fluxes() |
|---|
| 867 | |
|---|
| 868 | # Update timestep to fit yieldstep and finaltime |
|---|
| 869 | self.update_timestep(yieldstep, finaltime) |
|---|
| 870 | |
|---|
| 871 | # Update conserved quantities |
|---|
| 872 | self.update_conserved_quantities() |
|---|
| 873 | |
|---|
| 874 | # Update ghosts |
|---|
| 875 | self.update_ghosts() |
|---|
| 876 | |
|---|
| 877 | # Update vertex and edge values |
|---|
| 878 | self.distribute_to_vertices_and_edges() |
|---|
| 879 | |
|---|
| 880 | # Update boundary values |
|---|
| 881 | self.update_boundary() |
|---|
| 882 | |
|---|
| 883 | # Update time |
|---|
| 884 | self.time += self.timestep |
|---|
| 885 | |
|---|
| 886 | |
|---|
| 887 | |
|---|
| 888 | |
|---|
| 889 | def evolve_one_rk2_step(self, yieldstep, finaltime): |
|---|
| 890 | """ |
|---|
| 891 | One 2nd order RK timestep |
|---|
| 892 | Q^{n+1} = 0.5 Q^n + 0.5 E(h)^2 Q^n |
|---|
| 893 | """ |
|---|
| 894 | |
|---|
| 895 | # Save initial initial conserved quantities values |
|---|
| 896 | self.backup_conserved_quantities() |
|---|
| 897 | |
|---|
| 898 | #-------------------------------------- |
|---|
| 899 | # First euler step |
|---|
| 900 | #-------------------------------------- |
|---|
| 901 | |
|---|
| 902 | # Compute fluxes across each element edge |
|---|
| 903 | self.compute_fluxes() |
|---|
| 904 | |
|---|
| 905 | # Update timestep to fit yieldstep and finaltime |
|---|
| 906 | self.update_timestep(yieldstep, finaltime) |
|---|
| 907 | |
|---|
| 908 | # Update conserved quantities |
|---|
| 909 | self.update_conserved_quantities() |
|---|
| 910 | |
|---|
| 911 | # Update ghosts |
|---|
| 912 | self.update_ghosts() |
|---|
| 913 | |
|---|
| 914 | # Update vertex and edge values |
|---|
| 915 | self.distribute_to_vertices_and_edges() |
|---|
| 916 | |
|---|
| 917 | # Update boundary values |
|---|
| 918 | self.update_boundary() |
|---|
| 919 | |
|---|
| 920 | # Update time |
|---|
| 921 | self.time += self.timestep |
|---|
| 922 | |
|---|
| 923 | #------------------------------------ |
|---|
| 924 | # Second Euler step |
|---|
| 925 | #------------------------------------ |
|---|
| 926 | |
|---|
| 927 | # Compute fluxes across each element edge |
|---|
| 928 | self.compute_fluxes() |
|---|
| 929 | |
|---|
| 930 | # Update conserved quantities |
|---|
| 931 | self.update_conserved_quantities() |
|---|
| 932 | |
|---|
| 933 | #------------------------------------ |
|---|
| 934 | # Combine initial and final values |
|---|
| 935 | # of conserved quantities and cleanup |
|---|
| 936 | #------------------------------------ |
|---|
| 937 | |
|---|
| 938 | # Combine steps |
|---|
| 939 | self.saxpy_conserved_quantities(0.5, 0.5) |
|---|
| 940 | |
|---|
| 941 | #----------------------------------- |
|---|
| 942 | # clean up vertex values |
|---|
| 943 | #----------------------------------- |
|---|
| 944 | |
|---|
| 945 | # Update ghosts |
|---|
| 946 | self.update_ghosts() |
|---|
| 947 | |
|---|
| 948 | # Update vertex and edge values |
|---|
| 949 | self.distribute_to_vertices_and_edges() |
|---|
| 950 | |
|---|
| 951 | # Update boundary values |
|---|
| 952 | self.update_boundary() |
|---|
| 953 | |
|---|
| 954 | |
|---|
| 955 | |
|---|
| 956 | def evolve_one_rk3_step(self, yieldstep, finaltime): |
|---|
| 957 | """ |
|---|
| 958 | One 3rd order RK timestep |
|---|
| 959 | Q^(1) = 3/4 Q^n + 1/4 E(h)^2 Q^n (at time t^n + h/2) |
|---|
| 960 | Q^{n+1} = 1/3 Q^n + 2/3 E(h) Q^(1) (at time t^{n+1}) |
|---|
| 961 | """ |
|---|
| 962 | |
|---|
| 963 | # Save initial initial conserved quantities values |
|---|
| 964 | self.backup_conserved_quantities() |
|---|
| 965 | |
|---|
| 966 | initial_time = self.time |
|---|
| 967 | |
|---|
| 968 | #-------------------------------------- |
|---|
| 969 | # First euler step |
|---|
| 970 | #-------------------------------------- |
|---|
| 971 | |
|---|
| 972 | # Compute fluxes across each element edge |
|---|
| 973 | self.compute_fluxes() |
|---|
| 974 | |
|---|
| 975 | # Update timestep to fit yieldstep and finaltime |
|---|
| 976 | self.update_timestep(yieldstep, finaltime) |
|---|
| 977 | |
|---|
| 978 | # Update conserved quantities |
|---|
| 979 | self.update_conserved_quantities() |
|---|
| 980 | |
|---|
| 981 | # Update ghosts |
|---|
| 982 | self.update_ghosts() |
|---|
| 983 | |
|---|
| 984 | # Update vertex and edge values |
|---|
| 985 | self.distribute_to_vertices_and_edges() |
|---|
| 986 | |
|---|
| 987 | # Update boundary values |
|---|
| 988 | self.update_boundary() |
|---|
| 989 | |
|---|
| 990 | # Update time |
|---|
| 991 | self.time += self.timestep |
|---|
| 992 | |
|---|
| 993 | #------------------------------------ |
|---|
| 994 | # Second Euler step |
|---|
| 995 | #------------------------------------ |
|---|
| 996 | |
|---|
| 997 | # Compute fluxes across each element edge |
|---|
| 998 | self.compute_fluxes() |
|---|
| 999 | |
|---|
| 1000 | # Update conserved quantities |
|---|
| 1001 | self.update_conserved_quantities() |
|---|
| 1002 | |
|---|
| 1003 | #------------------------------------ |
|---|
| 1004 | #Combine steps to obtain intermediate |
|---|
| 1005 | #solution at time t^n + 0.5 h |
|---|
| 1006 | #------------------------------------ |
|---|
| 1007 | |
|---|
| 1008 | # Combine steps |
|---|
| 1009 | self.saxpy_conserved_quantities(0.25, 0.75) |
|---|
| 1010 | |
|---|
| 1011 | # Update ghosts |
|---|
| 1012 | self.update_ghosts() |
|---|
| 1013 | |
|---|
| 1014 | # Update vertex and edge values |
|---|
| 1015 | self.distribute_to_vertices_and_edges() |
|---|
| 1016 | |
|---|
| 1017 | # Update boundary values |
|---|
| 1018 | self.update_boundary() |
|---|
| 1019 | |
|---|
| 1020 | # Set substep time |
|---|
| 1021 | self.time = initial_time + self.timestep*0.5 |
|---|
| 1022 | |
|---|
| 1023 | #------------------------------------ |
|---|
| 1024 | # Third Euler step |
|---|
| 1025 | #------------------------------------ |
|---|
| 1026 | |
|---|
| 1027 | # Compute fluxes across each element edge |
|---|
| 1028 | self.compute_fluxes() |
|---|
| 1029 | |
|---|
| 1030 | # Update conserved quantities |
|---|
| 1031 | self.update_conserved_quantities() |
|---|
| 1032 | |
|---|
| 1033 | #------------------------------------ |
|---|
| 1034 | # Combine final and initial values |
|---|
| 1035 | # and cleanup |
|---|
| 1036 | #------------------------------------ |
|---|
| 1037 | |
|---|
| 1038 | # Combine steps |
|---|
| 1039 | self.saxpy_conserved_quantities(2.0/3.0, 1.0/3.0) |
|---|
| 1040 | |
|---|
| 1041 | # Update ghosts |
|---|
| 1042 | self.update_ghosts() |
|---|
| 1043 | |
|---|
| 1044 | # Update vertex and edge values |
|---|
| 1045 | self.distribute_to_vertices_and_edges() |
|---|
| 1046 | |
|---|
| 1047 | # Update boundary values |
|---|
| 1048 | self.update_boundary() |
|---|
| 1049 | |
|---|
| 1050 | # Set new time |
|---|
| 1051 | self.time = initial_time + self.timestep |
|---|
| 1052 | |
|---|
| 1053 | |
|---|
| 1054 | def backup_conserved_quantities(self): |
|---|
| 1055 | N = len(self) # Number_of_triangles |
|---|
| 1056 | |
|---|
| 1057 | # Backup conserved_quantities centroid values |
|---|
| 1058 | for name in self.conserved_quantities: |
|---|
| 1059 | Q = self.quantities[name] |
|---|
| 1060 | Q.backup_centroid_values() |
|---|
| 1061 | |
|---|
| 1062 | def saxpy_conserved_quantities(self,a,b): |
|---|
| 1063 | N = len(self) #number_of_triangles |
|---|
| 1064 | |
|---|
| 1065 | # Backup conserved_quantities centroid values |
|---|
| 1066 | for name in self.conserved_quantities: |
|---|
| 1067 | Q = self.quantities[name] |
|---|
| 1068 | Q.saxpy_centroid_values(a,b) |
|---|
| 1069 | |
|---|
| 1070 | |
|---|
| 1071 | #============================== |
|---|
| 1072 | # John Jakeman's old evolve code |
|---|
| 1073 | #============================= |
|---|
| 1074 | |
|---|
| 1075 | def evolve_john(self, yieldstep = None, finaltime = None, |
|---|
| 1076 | skip_initial_step = False): |
|---|
| 1077 | """Evolve model from time=0.0 to finaltime yielding results |
|---|
| 1078 | every yieldstep. |
|---|
| 1079 | |
|---|
| 1080 | Internally, smaller timesteps may be taken. |
|---|
| 1081 | |
|---|
| 1082 | Evolve is implemented as a generator and is to be called as such, e.g. |
|---|
| 1083 | |
|---|
| 1084 | for t in domain.evolve(timestep, yieldstep, finaltime): |
|---|
| 1085 | <Do something with domain and t> |
|---|
| 1086 | |
|---|
| 1087 | """ |
|---|
| 1088 | |
|---|
| 1089 | from config import min_timestep, max_timestep, epsilon |
|---|
| 1090 | |
|---|
| 1091 | #FIXME: Maybe lump into a larger check prior to evolving |
|---|
| 1092 | msg = 'Boundary tags must be bound to boundary objects before evolving system, ' |
|---|
| 1093 | msg += 'e.g. using the method set_boundary.\n' |
|---|
| 1094 | msg += 'This system has the boundary tags %s ' %self.get_boundary_tags() |
|---|
| 1095 | assert hasattr(self, 'boundary_objects'), msg |
|---|
| 1096 | |
|---|
| 1097 | # #self.set_defaults() |
|---|
| 1098 | |
|---|
| 1099 | if yieldstep is None: |
|---|
| 1100 | yieldstep = max_timestep |
|---|
| 1101 | else: |
|---|
| 1102 | yieldstep = float(yieldstep) |
|---|
| 1103 | |
|---|
| 1104 | self.order = self.default_order |
|---|
| 1105 | |
|---|
| 1106 | self.time_order = self.default_time_order |
|---|
| 1107 | |
|---|
| 1108 | self.yieldtime = 0.0 #Time between 'yields' |
|---|
| 1109 | |
|---|
| 1110 | #Initialise interval of timestep sizes (for reporting only) |
|---|
| 1111 | # SEEMS WIERD |
|---|
| 1112 | self.min_timestep = max_timestep |
|---|
| 1113 | self.max_timestep = min_timestep |
|---|
| 1114 | self.finaltime = finaltime |
|---|
| 1115 | self.number_of_steps = 0 |
|---|
| 1116 | self.number_of_first_order_steps = 0 |
|---|
| 1117 | |
|---|
| 1118 | #update ghosts |
|---|
| 1119 | self.update_ghosts() |
|---|
| 1120 | |
|---|
| 1121 | #Initial update of vertex and edge values |
|---|
| 1122 | self.distribute_to_vertices_and_edges() |
|---|
| 1123 | |
|---|
| 1124 | #Initial update boundary values |
|---|
| 1125 | self.update_boundary() |
|---|
| 1126 | |
|---|
| 1127 | #Or maybe restore from latest checkpoint |
|---|
| 1128 | if self.checkpoint is True: |
|---|
| 1129 | self.goto_latest_checkpoint() |
|---|
| 1130 | |
|---|
| 1131 | if skip_initial_step is False: |
|---|
| 1132 | yield(self.time) #Yield initial values |
|---|
| 1133 | |
|---|
| 1134 | while True: |
|---|
| 1135 | if self.time_order == 1: |
|---|
| 1136 | #Compute fluxes across each element edge |
|---|
| 1137 | self.compute_fluxes() |
|---|
| 1138 | #Update timestep to fit yieldstep and finaltime |
|---|
| 1139 | self.update_timestep(yieldstep, finaltime) |
|---|
| 1140 | #Compute forcing terms |
|---|
| 1141 | self.compute_forcing_terms() |
|---|
| 1142 | #Update conserved quantities |
|---|
| 1143 | self.update_conserved_quantities(self.timestep) |
|---|
| 1144 | #update ghosts |
|---|
| 1145 | #self.update_ghosts() |
|---|
| 1146 | #Update vertex and edge values |
|---|
| 1147 | self.distribute_to_vertices_and_edges() |
|---|
| 1148 | #Update boundary values |
|---|
| 1149 | self.update_boundary() |
|---|
| 1150 | |
|---|
| 1151 | elif self.time_order == 2: |
|---|
| 1152 | |
|---|
| 1153 | self.compute_timestep() #self.compute_fluxes() !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
|---|
| 1154 | |
|---|
| 1155 | #Solve inhomogeneous operator for half a timestep |
|---|
| 1156 | self.solve_inhomogenous_second_order(yieldstep, finaltime) |
|---|
| 1157 | |
|---|
| 1158 | #Solve homogeneous operator for full timestep using |
|---|
| 1159 | #Harten second order timestepping |
|---|
| 1160 | self.solve_homogenous_second_order(yieldstep,finaltime) |
|---|
| 1161 | |
|---|
| 1162 | #Solve inhomogeneous operator for half a timestep |
|---|
| 1163 | self.solve_inhomogenous_second_order(yieldstep, finaltime) |
|---|
| 1164 | |
|---|
| 1165 | #Update time |
|---|
| 1166 | self.time += self.timestep |
|---|
| 1167 | self.yieldtime += self.timestep |
|---|
| 1168 | self.number_of_steps += 1 |
|---|
| 1169 | if self.order == 1: |
|---|
| 1170 | self.number_of_first_order_steps += 1 |
|---|
| 1171 | |
|---|
| 1172 | #Yield results |
|---|
| 1173 | if finaltime is not None and abs(self.time - finaltime) < epsilon: |
|---|
| 1174 | |
|---|
| 1175 | #FIXME: There is a rare situation where the |
|---|
| 1176 | #final time step is stored twice. Can we make a test? |
|---|
| 1177 | |
|---|
| 1178 | # Yield final time and stop |
|---|
| 1179 | yield(self.time) |
|---|
| 1180 | break |
|---|
| 1181 | |
|---|
| 1182 | |
|---|
| 1183 | if abs(self.yieldtime - yieldstep) < epsilon: |
|---|
| 1184 | # Yield (intermediate) time and allow inspection of domain |
|---|
| 1185 | |
|---|
| 1186 | if self.checkpoint is True: |
|---|
| 1187 | self.store_checkpoint() |
|---|
| 1188 | self.delete_old_checkpoints() |
|---|
| 1189 | |
|---|
| 1190 | #Pass control on to outer loop for more specific actions |
|---|
| 1191 | yield(self.time) |
|---|
| 1192 | |
|---|
| 1193 | # Reinitialise |
|---|
| 1194 | self.yieldtime = 0.0 |
|---|
| 1195 | self.min_timestep = max_timestep |
|---|
| 1196 | self.max_timestep = min_timestep |
|---|
| 1197 | self.number_of_steps = 0 |
|---|
| 1198 | self.number_of_first_order_steps = 0 |
|---|
| 1199 | |
|---|
| 1200 | def solve_inhomogenous_second_order(self,yieldstep, finaltime): |
|---|
| 1201 | |
|---|
| 1202 | #Update timestep to fit yieldstep and finaltime |
|---|
| 1203 | self.update_timestep(yieldstep, finaltime) |
|---|
| 1204 | #Compute forcing terms |
|---|
| 1205 | self.compute_forcing_terms() |
|---|
| 1206 | #Update conserved quantities |
|---|
| 1207 | self.update_conserved_quantities(0.5*self.timestep) |
|---|
| 1208 | #Update vertex and edge values |
|---|
| 1209 | self.distribute_to_vertices_and_edges() |
|---|
| 1210 | #Update boundary values |
|---|
| 1211 | self.update_boundary() |
|---|
| 1212 | |
|---|
| 1213 | def solve_homogenous_second_order(self,yieldstep,finaltime): |
|---|
| 1214 | """Use Shu Second order timestepping to update |
|---|
| 1215 | conserved quantities |
|---|
| 1216 | |
|---|
| 1217 | q^{n+1/2} = q^{n}+0.5*dt*F^{n} |
|---|
| 1218 | q^{n+1} = q^{n}+dt*F^{n+1/2} |
|---|
| 1219 | """ |
|---|
| 1220 | import copy |
|---|
| 1221 | from Numeric import zeros,Float |
|---|
| 1222 | |
|---|
| 1223 | N = self.number_of_elements |
|---|
| 1224 | |
|---|
| 1225 | self.compute_fluxes() |
|---|
| 1226 | #Update timestep to fit yieldstep and finaltime |
|---|
| 1227 | self.update_timestep(yieldstep, finaltime) |
|---|
| 1228 | #Compute forcing terms |
|---|
| 1229 | #NOT NEEDED FOR 2ND ORDER STRANG SPLIITING |
|---|
| 1230 | #ADDING THIS WILL NEED TO REMOVE ZEROING IN COMPUTE_FORCING |
|---|
| 1231 | #self.compute_forcing_terms() |
|---|
| 1232 | |
|---|
| 1233 | QC = zeros((N,len(self.conserved_quantities)),Float) |
|---|
| 1234 | QF = zeros((N,len(self.conserved_quantities)),Float) |
|---|
| 1235 | |
|---|
| 1236 | i = 0 |
|---|
| 1237 | for name in self.conserved_quantities: |
|---|
| 1238 | Q = self.quantities[name] |
|---|
| 1239 | #Store the centroid values at time t^n |
|---|
| 1240 | QC[:,i] = copy.copy(Q.centroid_values) |
|---|
| 1241 | QF[:,i] = copy.copy(Q.explicit_update) |
|---|
| 1242 | #Update conserved quantities |
|---|
| 1243 | Q.update(self.timestep) |
|---|
| 1244 | i+=1 |
|---|
| 1245 | |
|---|
| 1246 | #Update vertex and edge values |
|---|
| 1247 | self.distribute_to_vertices_and_edges() |
|---|
| 1248 | #Update boundary values |
|---|
| 1249 | self.update_boundary() |
|---|
| 1250 | |
|---|
| 1251 | self.compute_fluxes() |
|---|
| 1252 | self.update_timestep(yieldstep, finaltime) |
|---|
| 1253 | #Compute forcing terms |
|---|
| 1254 | #NOT NEEDED FOR 2ND ORDER STRANG SPLIITING |
|---|
| 1255 | #self.compute_forcing_terms() |
|---|
| 1256 | |
|---|
| 1257 | i = 0 |
|---|
| 1258 | for name in self.conserved_quantities: |
|---|
| 1259 | Q = self.quantities[name] |
|---|
| 1260 | Q.centroid_values = QC[:,i] |
|---|
| 1261 | Q.explicit_update = 0.5*(Q.explicit_update+QF[:,i]) |
|---|
| 1262 | #Update conserved quantities |
|---|
| 1263 | Q.update(self.timestep) |
|---|
| 1264 | i+=1 |
|---|
| 1265 | |
|---|
| 1266 | #Update vertex and edge values |
|---|
| 1267 | self.distribute_to_vertices_and_edges() |
|---|
| 1268 | #Update boundary values |
|---|
| 1269 | self.update_boundary() |
|---|
| 1270 | |
|---|
| 1271 | def solve_homogenous_second_order_harten(self,yieldstep,finaltime): |
|---|
| 1272 | """Use Harten Second order timestepping to update |
|---|
| 1273 | conserved quantities |
|---|
| 1274 | |
|---|
| 1275 | q^{n+1/2} = q^{n}+0.5*dt*F^{n} |
|---|
| 1276 | q^{n+1} = q^{n}+dt*F^{n+1/2} |
|---|
| 1277 | """ |
|---|
| 1278 | import copy |
|---|
| 1279 | from Numeric import zeros,Float |
|---|
| 1280 | |
|---|
| 1281 | N = self.number_of_elements |
|---|
| 1282 | |
|---|
| 1283 | self.compute_fluxes() |
|---|
| 1284 | #Update timestep to fit yieldstep and finaltime |
|---|
| 1285 | self.update_timestep(yieldstep, finaltime) |
|---|
| 1286 | #Compute forcing terms |
|---|
| 1287 | #NOT NEEDED FOR 2ND ORDER STRANG SPLIITING |
|---|
| 1288 | #ADDING THIS WILL NEED TO REMOVE ZEROING IN COMPUTE_FORCING |
|---|
| 1289 | #self.compute_forcing_terms() |
|---|
| 1290 | |
|---|
| 1291 | QC = zeros((N,len(self.conserved_quantities)),Float) |
|---|
| 1292 | |
|---|
| 1293 | i = 0 |
|---|
| 1294 | for name in self.conserved_quantities: |
|---|
| 1295 | Q = self.quantities[name] |
|---|
| 1296 | #Store the centroid values at time t^n |
|---|
| 1297 | QC[:,i] = copy.copy(Q.centroid_values) |
|---|
| 1298 | #Update conserved quantities |
|---|
| 1299 | Q.update(0.5*self.timestep) |
|---|
| 1300 | i+=1 |
|---|
| 1301 | |
|---|
| 1302 | #Update vertex and edge values |
|---|
| 1303 | self.distribute_to_vertices_and_edges() |
|---|
| 1304 | #Update boundary values |
|---|
| 1305 | self.update_boundary() |
|---|
| 1306 | |
|---|
| 1307 | self.compute_fluxes() |
|---|
| 1308 | self.update_timestep(yieldstep, finaltime) |
|---|
| 1309 | #Compute forcing terms |
|---|
| 1310 | #NOT NEEDED FOR 2ND ORDER STRANG SPLIITING |
|---|
| 1311 | #self.compute_forcing_terms() |
|---|
| 1312 | |
|---|
| 1313 | i = 0 |
|---|
| 1314 | for name in self.conserved_quantities: |
|---|
| 1315 | Q = self.quantities[name] |
|---|
| 1316 | Q.centroid_values = QC[:,i] |
|---|
| 1317 | #Update conserved quantities |
|---|
| 1318 | Q.update(self.timestep) |
|---|
| 1319 | i+=1 |
|---|
| 1320 | |
|---|
| 1321 | #Update vertex and edge values |
|---|
| 1322 | self.distribute_to_vertices_and_edges() |
|---|
| 1323 | #Update boundary values |
|---|
| 1324 | self.update_boundary() |
|---|
| 1325 | |
|---|
| 1326 | def distribute_to_vertices_and_edges(self): |
|---|
| 1327 | """Extrapolate conserved quantities from centroid to |
|---|
| 1328 | vertices and edge-midpoints for each volume |
|---|
| 1329 | |
|---|
| 1330 | Default implementation is straight first order, |
|---|
| 1331 | i.e. constant values throughout each element and |
|---|
| 1332 | no reference to non-conserved quantities. |
|---|
| 1333 | """ |
|---|
| 1334 | |
|---|
| 1335 | for name in self.conserved_quantities: |
|---|
| 1336 | Q = self.quantities[name] |
|---|
| 1337 | if self.order == 1: |
|---|
| 1338 | Q.extrapolate_first_order() |
|---|
| 1339 | elif self.order == 2: |
|---|
| 1340 | Q.extrapolate_second_order() |
|---|
| 1341 | #Q.limit() |
|---|
| 1342 | else: |
|---|
| 1343 | raise 'Unknown order' |
|---|
| 1344 | #Q.interpolate_from_vertices_to_edges() |
|---|
| 1345 | |
|---|
| 1346 | |
|---|
| 1347 | def update_ghosts(self): |
|---|
| 1348 | pass |
|---|
| 1349 | |
|---|
| 1350 | def update_boundary(self): |
|---|
| 1351 | """Go through list of boundary objects and update boundary values |
|---|
| 1352 | for all conserved quantities on boundary. |
|---|
| 1353 | """ |
|---|
| 1354 | |
|---|
| 1355 | #FIXME: Update only those that change (if that can be worked out) |
|---|
| 1356 | #FIXME: Boundary objects should not include ghost nodes. |
|---|
| 1357 | #for i, ((vol_id, edge_id), B) in enumerate(self.boundary_objects): |
|---|
| 1358 | # q = B.evaluate(vol_id, edge_id) |
|---|
| 1359 | for i, ((vol_id, vertex_id), B) in enumerate(self.boundary_objects): |
|---|
| 1360 | q = B.evaluate(vol_id, vertex_id) |
|---|
| 1361 | |
|---|
| 1362 | for j, name in enumerate(self.conserved_quantities): |
|---|
| 1363 | Q = self.quantities[name] |
|---|
| 1364 | Q.boundary_values[i] = q[j] |
|---|
| 1365 | |
|---|
| 1366 | def update_timestep(self, yieldstep, finaltime): |
|---|
| 1367 | |
|---|
| 1368 | from config import min_timestep |
|---|
| 1369 | |
|---|
| 1370 | # self.timestep is calculated from speed of characteristics |
|---|
| 1371 | # Apply CFL condition here |
|---|
| 1372 | timestep = self.CFL*self.timestep |
|---|
| 1373 | |
|---|
| 1374 | #Record maximal and minimal values of timestep for reporting |
|---|
| 1375 | self.max_timestep = max(timestep, self.max_timestep) |
|---|
| 1376 | self.min_timestep = min(timestep, self.min_timestep) |
|---|
| 1377 | |
|---|
| 1378 | #Protect against degenerate time steps |
|---|
| 1379 | if timestep < min_timestep: |
|---|
| 1380 | |
|---|
| 1381 | #Number of consecutive small steps taken b4 taking action |
|---|
| 1382 | self.smallsteps += 1 |
|---|
| 1383 | |
|---|
| 1384 | if self.smallsteps > self.max_smallsteps: |
|---|
| 1385 | self.smallsteps = 0 #Reset |
|---|
| 1386 | |
|---|
| 1387 | if self.order == 1: |
|---|
| 1388 | msg = 'WARNING: Too small timestep %.16f reached '\ |
|---|
| 1389 | %timestep |
|---|
| 1390 | msg += 'even after %d steps of 1 order scheme'\ |
|---|
| 1391 | %self.max_smallsteps |
|---|
| 1392 | print msg |
|---|
| 1393 | timestep = min_timestep #Try enforcing min_step |
|---|
| 1394 | |
|---|
| 1395 | #raise msg |
|---|
| 1396 | else: |
|---|
| 1397 | #Try to overcome situation by switching to 1 order |
|---|
| 1398 | print "changing Order 1" |
|---|
| 1399 | self.order = 1 |
|---|
| 1400 | |
|---|
| 1401 | else: |
|---|
| 1402 | self.smallsteps = 0 |
|---|
| 1403 | if self.order == 1 and self.default_order == 2: |
|---|
| 1404 | self.order = 2 |
|---|
| 1405 | |
|---|
| 1406 | |
|---|
| 1407 | #Ensure that final time is not exceeded |
|---|
| 1408 | if finaltime is not None and self.time + timestep > finaltime: |
|---|
| 1409 | timestep = finaltime-self.time |
|---|
| 1410 | |
|---|
| 1411 | #Ensure that model time is aligned with yieldsteps |
|---|
| 1412 | if self.yieldtime + timestep > yieldstep: |
|---|
| 1413 | timestep = yieldstep-self.yieldtime |
|---|
| 1414 | |
|---|
| 1415 | self.timestep = timestep |
|---|
| 1416 | |
|---|
| 1417 | def update_extrema(self): |
|---|
| 1418 | pass |
|---|
| 1419 | |
|---|
| 1420 | def compute_forcing_terms(self): |
|---|
| 1421 | """If there are any forcing functions driving the system |
|---|
| 1422 | they should be defined in Domain subclass and appended to |
|---|
| 1423 | the list self.forcing_terms |
|---|
| 1424 | """ |
|---|
| 1425 | #Clears explicit_update needed for second order method |
|---|
| 1426 | if self.time_order == 2: |
|---|
| 1427 | for name in self.conserved_quantities: |
|---|
| 1428 | Q = self.quantities[name] |
|---|
| 1429 | Q.explicit_update[:] = 0.0 |
|---|
| 1430 | |
|---|
| 1431 | for f in self.forcing_terms: |
|---|
| 1432 | f(self) |
|---|
| 1433 | |
|---|
| 1434 | |
|---|
| 1435 | def update_derived_quantites(self): |
|---|
| 1436 | pass |
|---|
| 1437 | |
|---|
| 1438 | #def update_conserved_quantities(self): |
|---|
| 1439 | def update_conserved_quantities(self,timestep): |
|---|
| 1440 | """Update vectors of conserved quantities using previously |
|---|
| 1441 | computed fluxes specified forcing functions. |
|---|
| 1442 | """ |
|---|
| 1443 | |
|---|
| 1444 | from Numeric import ones, sum, equal, Float |
|---|
| 1445 | |
|---|
| 1446 | N = self.number_of_elements |
|---|
| 1447 | d = len(self.conserved_quantities) |
|---|
| 1448 | |
|---|
| 1449 | #timestep = self.timestep |
|---|
| 1450 | |
|---|
| 1451 | #Compute forcing terms |
|---|
| 1452 | #self.compute_forcing_terms() |
|---|
| 1453 | |
|---|
| 1454 | #Update conserved_quantities |
|---|
| 1455 | for name in self.conserved_quantities: |
|---|
| 1456 | Q = self.quantities[name] |
|---|
| 1457 | Q.update(timestep) |
|---|
| 1458 | |
|---|
| 1459 | #Clean up |
|---|
| 1460 | #Note that Q.explicit_update is reset by compute_fluxes |
|---|
| 1461 | |
|---|
| 1462 | #MH090605 commented out the following since semi_implicit_update is now re-initialized |
|---|
| 1463 | #at the end of the _update function in quantity_ext.c (This is called by the |
|---|
| 1464 | #preceeding Q.update(timestep) statement above). |
|---|
| 1465 | #For run_profile.py with N=128, the time of update_conserved_quantities is cut from 14.00 secs |
|---|
| 1466 | #to 8.35 secs |
|---|
| 1467 | |
|---|
| 1468 | #Q.semi_implicit_update[:] = 0.0 |
|---|
| 1469 | |
|---|
| 1470 | if __name__ == "__main__": |
|---|
| 1471 | |
|---|
| 1472 | points1 = [0.0, 1.0, 2.0, 3.0] |
|---|
| 1473 | D1 = Domain(points1) |
|---|
| 1474 | |
|---|
| 1475 | print D1.get_coordinate(0) |
|---|
| 1476 | print D1.get_coordinate(0,1) |
|---|
| 1477 | print 'Number of Elements = ',D1.number_of_elements |
|---|
| 1478 | |
|---|
| 1479 | try: |
|---|
| 1480 | print D1.get_coordinate(3) |
|---|
| 1481 | except: |
|---|
| 1482 | pass |
|---|
| 1483 | else: |
|---|
| 1484 | msg = 'Should have raised an out of bounds exception' |
|---|
| 1485 | raise msg |
|---|
| 1486 | |
|---|
| 1487 | #points2 = [0.0, 1.0, 2.0, 3.0, 2.5] |
|---|
| 1488 | #D2 = Domain(points2) |
|---|
