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annotate +rv/constructDiffOps.m @ 1154:3108963cc42c feature/rv

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Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 06 Mar 2019 09:45:52 +0100
parents 52f59d27b40f
children 8c0e2b50f018 82315fa6adb1
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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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.
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1026
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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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3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1146
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3 [D, solutionPenalties] = constructFluxDiffOp(scheme, g, order, schemeParams, opSet, BCs);
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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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parents: 1026
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4 D2 = constructSymmetricD2Operator(g, order, opSet);
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5 D_rv = @(v,Viscosity)(D(v) + D2(Viscosity)*v);
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6
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7 %% DiffOps for residual viscosity
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8 [D_flux, residualPenalties] = constructFluxDiffOp(scheme, g, max(order-2,2), schemeParams, opSet, BCs);
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9 % DiffOp for flux in residual viscosity. Due to sign conventions of the implemnted schemes, we need to
5359a61cb4d9 Add utility for constructing the operators used by a discretization emplying RV-stabilization
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10 % change the sign.
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parents: 1026
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11 D_flux = @(v) -D_flux(v);
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12 % DiffOp for time derivative in residual viscosity
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13 DvDt = D;
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14 end
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15
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16 function [D, penalties] = constructFluxDiffOp(scheme, g, order, schemeParams, opSet, BCs)
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17 diffOp = scheme(g, order, schemeParams{:}, opSet);
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18 [D, penalties] = addClosuresToDiffOp(diffOp, BCs);
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19 end
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21 function [D, penalties] = addClosuresToDiffOp(diffOp, BCs)
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22 if ~isa(diffOp.D, 'function_handle')
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23 D = @(v) diffOp.D*v;
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24 else
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25 D = diffOp.D;
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26 end
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27 penalties = cell(size(BCs));
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28 for i = 1:size(BCs,1)
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29 for j = 1:size(BCs,2)
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30 [closure, penalties{i,j}] = diffOp.boundary_condition(BCs{i,j}.boundary, BCs{i,j}.type);
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parents: 1026
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31 if ~isa(closure, 'function_handle')
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32 closure = @(v) closure*v;
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33 end
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34 D = @(v) D(v) + closure(v);
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35 end
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36 end
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37 end
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38
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39 function D2 = constructSymmetricD2Operator(g, order, opSet)
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40
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41
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42 m = g.size();
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43 ops = cell(g.D(),1);
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44 I = cell(g.D(),1);
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parents: 1026
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45 for i = 1:g.D()
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46 lim = {g.x{i}(1), g.x{i}(end)};
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47 ops{i} = opSet(m(i), lim, order);
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48 I{i} = speye(m(i));
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49 end
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50
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51 switch g.D()
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52 case 1
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53 e_r = ops{1}.e_r;
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54 e_l = ops{1}.e_l;
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55 Hi = ops{1}.HI;
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56 B = e_r*e_r' - e_l*e_l';
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57 if isequal(opSet,@sbp.D1Upwind)
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parents: 1026
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58 Dm = ops{1}.Dm;
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59 Dp = ops{1}.Dp;
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60 M = Dm - Hi*B;
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61 D2 = @(Viscosity) M*Viscosity*Dp;
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62 else
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63 % TODO: Fix closure for D2Variable
3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
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64 D2 = @(Viscosity)ops{1}.D2(Viscosity);
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65 end
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66 case 2
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67 % TODO:
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68 % Currently only implemented for upwind operators.
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69 % Remove this part once the time-dependent D2 operator is implemented for other opSets
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parents: 1026
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70 % or if it is decided that it should only be supported for upwind operators.
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71 assert(isequal(opSet,@sbp.D1Upwind))
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72 e_e = kron(ops{1}.e_r,I{2});
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73 e_w = kron(ops{1}.e_l,I{2});
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74 Dm_x = kron(ops{1}.Dm,I{2});
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75 Dp_x = kron(ops{1}.Dp,I{2});
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76 H_x = kron(ops{1}.HI,I{2});
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77 B_x = e_e*e_e' - e_w*e_w';
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78 M_x = Dm_x-H_x*B_x;
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79 D2_x = @(Viscosity) M_x*Viscosity*Dp_x;
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80
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81 e_n = kron(I{1},ops{2}.e_r);
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82 e_s = kron(I{1},ops{2}.e_l);
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83 Dm_y = kron(I{1},ops{2}.Dm);
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84 Dp_y = kron(I{1},ops{2}.Dp);
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85 H_y = kron(I{1},ops{2}.HI);
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86 B_y = e_n*e_n' - e_s*e_s';
1154
3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1146
diff changeset
87 M_y = Dm_y-H_y*B_y;
3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1146
diff changeset
88 D2_y = @(Viscosity) M_y*Viscosity*Dp_y;
3108963cc42c Improve efficiency of diffOps in Burgers2d, the artificial diffusion operator in rv.constructDiffOps and the RungekuttaExteriorRv time-steppers
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1146
diff changeset
89 D2 = @(Viscosity) D2_x(Viscosity) + D2_y(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
90 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
91 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
92 end
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 end