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annotate +rv/constructDiffOps.m @ 1157:82315fa6adb1 feature/rv

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Add residual order as an input argument to constructDiffOps
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Tue, 25 Jun 2019 13:24:01 +0200
parents 3108963cc42c
children 76e3bb7836cf
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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82315fa6adb1 Add residual order as an input argument to constructDiffOps
Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents: 1154
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1 function [D_rv, D_flux, DvDt, solutionPenalties, residualPenalties] = constructDiffOps(scheme, g, schemeOrder, residualOrder, schemeParams, opSet, BCs)
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2 %% DiffOps for solution vector
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3 [D, solutionPenalties] = constructFluxDiffOp(scheme, g, schemeOrder, schemeParams, opSet, BCs);
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4 D2 = constructSymmetricD2Operator(g, schemeOrder, 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, residualOrder, schemeParams, opSet, BCs);
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9 % TODO: Construct D_flux without closures when using bdfs.
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10 % diffOp = scheme(g, residualOrder, schemeParams{:}, opSet);
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11 % if ~isa(diffOp.D, 'function_handle')
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12 % D_flux = @(v) diffOp.D*v;
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13 % else
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14 % D_flux = diffOp.D;
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15 % end
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16
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17 % DiffOp for flux in residual viscosity. Due to sign conventions of the implemented schemes, we need to
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18 % change the sign.
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19 D_flux = @(v) -D_flux(v);
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20 % DiffOp for time derivative in residual viscosity
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21 DvDt = D;
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22 end
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23
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24 function [D, penalties] = constructFluxDiffOp(scheme, g, order, schemeParams, opSet, BCs)
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25 diffOp = scheme(g, order, schemeParams{:}, opSet);
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26 [D, penalties] = addClosuresToDiffOp(diffOp, BCs);
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27 end
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28
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29 function [D, penalties] = addClosuresToDiffOp(diffOp, BCs)
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30 if ~isa(diffOp.D, 'function_handle')
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31 D = @(v) diffOp.D*v;
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32 else
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33 D = diffOp.D;
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34 end
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35 penalties = cell(size(BCs));
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36 for i = 1:size(BCs,1)
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37 for j = 1:size(BCs,2)
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38 [closure, penalties{i,j}] = diffOp.boundary_condition(BCs{i,j}.boundary, BCs{i,j}.type);
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39 if ~isa(closure, 'function_handle')
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40 closure = @(v) closure*v;
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41 end
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42 D = @(v) D(v) + closure(v);
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43 end
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44 end
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45 end
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46
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47 function D2 = constructSymmetricD2Operator(g, order, opSet)
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48 m = g.size();
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49 ops = cell(g.D(),1);
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50 I = cell(g.D(),1);
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51 for i = 1:g.D()
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52 lim = {g.x{i}(1), g.x{i}(end)};
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53 ops{i} = opSet(m(i), lim, order);
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54 I{i} = speye(m(i));
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55 end
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56
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57 switch g.D()
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58 case 1
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59 e_r = ops{1}.e_r;
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60 e_l = ops{1}.e_l;
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61 Hi = ops{1}.HI;
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62 B = e_r*e_r' - e_l*e_l';
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63 if isequal(opSet,@sbp.D1Upwind)
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64 Dm = ops{1}.Dm;
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65 Dp = ops{1}.Dp;
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66 M = Dm - Hi*B;
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67 D2 = @(Viscosity) M*Viscosity*Dp;
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68 else
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69 % TODO: Fix closure for D2Variable
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70 % TODO: Fix Viscosity not being vector
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71 D2 = @(Viscosity)ops{1}.D2(diag(Viscosity));
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72 end
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73 case 2
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74 % TODO:
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75 % Currently only implemented for upwind operators.
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76 % Remove this part once the time-dependent D2 operator is implemented for other opSets
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77 % or if it is decided that it should only be supported for upwind operators.
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78 assert(isequal(opSet,@sbp.D1Upwind))
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79 e_e = kron(ops{1}.e_r,I{2});
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80 e_w = kron(ops{1}.e_l,I{2});
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81 Dm_x = kron(ops{1}.Dm,I{2});
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82 Dp_x = kron(ops{1}.Dp,I{2});
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83 H_x = kron(ops{1}.HI,I{2});
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84 B_x = e_e*e_e' - e_w*e_w';
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85 M_x = Dm_x-H_x*B_x;
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86 D2_x = @(Viscosity) M_x*Viscosity*Dp_x;
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87
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88 e_n = kron(I{1},ops{2}.e_r);
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89 e_s = kron(I{1},ops{2}.e_l);
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90 Dm_y = kron(I{1},ops{2}.Dm);
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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91 Dp_y = kron(I{1},ops{2}.Dp);
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92 H_y = kron(I{1},ops{2}.HI);
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diff changeset
93 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
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94 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
95 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
96 D2 = @(Viscosity) D2_x(Viscosity) + D2_y(Viscosity);
1020
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parents:
diff changeset
97 otherwise
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98 error('3D not yet implemented')
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
parents:
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99 end
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Vidar Stiernström <vidar.stiernstrom@it.uu.se>
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100 end