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annotate +rv/constructDiffOps.m @ 1223:9fddc8749445 rv_diffOp_test

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Closing branch
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Mon, 05 Aug 2019 10:48:37 +0200
parents 0c906f7ab8bf
children
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rev   line source
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2d7ba44340d0 Pass scheme specific parameters as cell array. This will enabale constructDiffOps to be more general. In addition, allow for schemes returning function handles as diffOps, which is currently how non-linear schemes such as Burgers1d are implemented.
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1 function [D_rv, D_flux, DvDt, solutionPenalties, residualPenalties] = constructDiffOps(scheme, g, order, schemeParams, opSet, BCs)
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2 %% DiffOps for solution vector
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3 [D, solutionPenalties] = constructTotalFluxDiffOp(scheme, g, order, schemeParams, opSet, BCs);
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4 D2 = constructSymmetricD2Operator(g, order, opSet);
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5
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6 if isa(D, 'function_handle')
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7 D_rv = @(v,viscosity)(D(v) + D2(viscosity))*v;
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8 [D_flux, residualPenalties] = constructTotalFluxDiffOp(scheme, g, max(order-2,2), schemeParams, opSet, BCs);
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9 D_flux = @(v) -D_flux(v)*v;
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10 DvDt = @(v)D(v)*v;
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11 else
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12 D_rv = @(v,viscosity)(D + D2(viscosity))*v;
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13 [D_flux, residualPenalties] = constructTotalFluxDiffOp(scheme, g, max(order-2,2), schemeParams, opSet, BCs);
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14 D_flux = @(v) -D_flux*v;
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15 DvDt = @(v)D*v;
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16 end
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17
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18 %% DiffOps for residual viscosity
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19
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20 % DiffOp for flux in residual viscosity. Due to sign conventions of the implemnted schemes, we need to
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21 % change the sign.
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22
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23 % DiffOp for time derivative in residual viscosity
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24
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25 end
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26
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27 function [D, penalties] = constructTotalFluxDiffOp(scheme, g, order, schemeParams, opSet, BCs)
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28 diffOp = scheme(g, order, schemeParams{:}, opSet);
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29 if isa(diffOp.D, 'function_handle')
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30 [D, penalties] = addClosuresToDiffOpFunction(diffOp, BCs);
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31 else
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32 [D, penalties] = addClosuresToDiffOp(diffOp, BCs);
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33 end
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34 end
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35
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36 function [D, penalties] = addClosuresToDiffOp(diffOp, BCs)
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37 penalties = cell(size(BCs));
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38 D = diffOp.D;
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39 for i = 1:size(BCs,1)
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40 for j = 1:size(BCs,2)
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41 [closure, penalties{i,j}] = diffOp.boundary_condition(BCs{i,j}.boundary, BCs{i,j}.type);
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42 D = D + closure;
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43 end
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44 end
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45
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46 end
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47
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48 function [D, penalties] = addClosuresToDiffOpFunction(diffOp, BCs)
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49 penalties = cell(size(BCs));
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50 D = diffOp.D;
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51 for i = 1:size(BCs,1)
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52 for j = 1:size(BCs,2)
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53 [closure, penalties{i,j}] = diffOp.boundary_condition(BCs{i,j}.boundary, BCs{i,j}.type);
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54 D = @(v) D(v) + closure(v);
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55 end
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56 end
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57
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59
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60 function D2 = constructSymmetricD2Operator(g, order, opSet)
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61 m = g.size();
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62 ops = cell(g.D(),1);
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63 I = cell(g.D(),1);
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64 for i = 1:g.D()
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65 lim = {g.x{i}(1), g.x{i}(end)};
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66 ops{i} = opSet(m(i), lim, order);
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67 I{i} = speye(m(i));
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68 end
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69
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70 switch g.D()
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71 case 1
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72 e_r = ops{1}.e_r;
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73 e_l = ops{1}.e_l;
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74 Hi = ops{1}.HI;
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75 B = e_r*e_r' - e_l*e_l';
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76 if isequal(opSet,@sbp.D1Upwind)
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77 Dm = ops{1}.Dm;
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78 Dp = ops{1}.Dp;
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79 HiB = Hi*B;
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80 D2 = @(viscosity) Dm*spdiag(viscosity)*Dp-HiB*spdiag(viscosity)*Dp;
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81 else
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82 D2 = @(viscosity)ops{1}.D2(viscosity);
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83 end
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84 case 2
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85 % TODO:
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86 % Currently only implemented for upwind operators.
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87 % Remove this part once the time-dependent D2 operator is implemented for other opSets
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88 % or if it is decided that it should only be supported for upwind operators.
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89 assert(isequal(opSet,@sbp.D1Upwind))
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
90 e_e = kron(ops{1}.e_r,I{2});
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
91 e_w = kron(ops{1}.e_l,I{2});
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
92 Dm_x = kron(ops{1}.Dm,I{2});
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
93 Dp_x = kron(ops{1}.Dp,I{2});
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
94 H_x = kron(ops{1}.HI,I{2});
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
95 B_x = e_e*e_e' - e_w*e_w';
1221
0c906f7ab8bf Attempt to reduce unnessecary operations when using the RV diffOps. Does not seem to improve efficiency at this stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1146
diff changeset
96 H_xB = H_x*B_x;
0c906f7ab8bf Attempt to reduce unnessecary operations when using the RV diffOps. Does not seem to improve efficiency at this stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1146
diff changeset
97 D2_x = @(viscosity) (Dm_x*spdiag(viscosity)-H_xB*spdiag(viscosity))*Dp_x;
1020
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
98
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
99 e_n = kron(I{1},ops{2}.e_r);
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
100 e_s = kron(I{1},ops{2}.e_l);
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
101 Dm_y = kron(I{1},ops{2}.Dm);
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
102 Dp_y = kron(I{1},ops{2}.Dp);
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
103 H_y = kron(I{1},ops{2}.HI);
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
104 B_y = e_n*e_n' - e_s*e_s';
1221
0c906f7ab8bf Attempt to reduce unnessecary operations when using the RV diffOps. Does not seem to improve efficiency at this stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1146
diff changeset
105 H_yB = H_y*B_y;
0c906f7ab8bf Attempt to reduce unnessecary operations when using the RV diffOps. Does not seem to improve efficiency at this stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1146
diff changeset
106 D2_y = @(viscosity) (Dm_y*spdiag(viscosity)-H_yB*spdiag(viscosity))*Dp_y;
1020
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
107 D2 = @(viscosity)D2_x(viscosity) + D2_y(viscosity);
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
108 otherwise
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
109 error('3D not yet implemented')
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
110 end
1221
0c906f7ab8bf Attempt to reduce unnessecary operations when using the RV diffOps. Does not seem to improve efficiency at this stage.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1146
diff changeset
111 D2 = @(viscosity) D2(viscosity);
1020
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
diff changeset
112 end