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Add utility function for constructing a (possibly multidimensional) grid based on the grid points used by the boundary optimized SBP operators
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Wed, 01 Jul 2020 15:15:30 +0200
parents 27ce3f653aa7
children
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1 % Interpolation operators by Mattsson and Carpenter (MC), see
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2 % Mattsson and Carpenter,
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3 % "Stable and Accurate Interpolatino Operators for High-Order Multiblock Finite DIfference Methods",
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4 % https://epubs.siam.org/doi/pdf/10.1137/090750068
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5 %
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6 % Let ^* denote the adjoint. These operators satsify
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7 %
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8 % Iuv2 = Iv2u^*
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9 %
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10 % Both Iu2v and Iv2u have p:th order accuracy, if the interior stencil is
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11 % of order 2p.
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12 %
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13 % This approach leads to a reduction of the convergence rate by one order for
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14 % PDEs with 2nd derivatives in space, as compared to conforming interfaces.
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15 % To obtain full convergence rate, use the order-preserving (OP) operators in
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16 % InterpOpsOP.m
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17 classdef InterpOpsMC < sbp.InterpOps
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18 properties
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20 % Structs of interpolation operators, fields .good and .bad
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21 % Here .good and .bad are the same, but this makes them fit in the
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22 % OP (order-preserving) framework.
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23 Iu2v
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24 Iv2u
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25 end
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27 methods
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28 % m_u, m_v -- number of grid points along the interface
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29 % order_u, order_v -- order of accuracy in the different blocks
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30 function obj = InterpOpsMC(m_u, m_v, order_u, order_v)
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32 assert(order_u == order_v,...
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33 'InterpOpsMC: Different orders of accuracy not available');
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35 switch order_u
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36 case 2
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37 intOpSet = @sbp.implementations.intOpMC_orders_2to2_ratio2to1;
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38 case 4
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39 intOpSet = @sbp.implementations.intOpMC_orders_4to4_ratio2to1;
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40 case 6
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41 intOpSet = @sbp.implementations.intOpMC_orders_6to6_ratio2to1;
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42 case 8
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43 intOpSet = @sbp.implementations.intOpMC_orders_8to8_ratio2to1;
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44 otherwise
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45 error('InterpOpsMC: Order of accuracy %d not available.', order_u);
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46 end
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48 Iu2v = struct;
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49 Iv2u = struct;
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50
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51 if (m_u-1)/(m_v-1) == 2
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52 % Block u is fine, v is coarse
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53 m_C = m_v;
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54 [Iv2u.good, Iu2v.bad] = intOpSet(m_C);
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55 Iv2u.bad = Iv2u.good;
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56 Iu2v.good = Iu2v.bad;
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57
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58 elseif (m_v-1)/(m_u-1) == 2
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59 % Block v is fine, u is coarse
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60 m_C = m_u;
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61 [Iu2v.good, Iv2u.bad] = intOpSet(m_C);
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62 Iu2v.bad = Iu2v.good;
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63 Iv2u.good = Iv2u.bad;
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64 else
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65 error('InterpOpsMC: Interpolation operators for grid ratio %f have not yet been constructed', (m_u-1)/(m_v-1));
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66 end
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68 obj.Iu2v = Iu2v;
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69 obj.Iv2u = Iv2u;
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71 end
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73 function str = string(obj)
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74 str = [class(obj)];
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75 end
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77 end
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78 end