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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 % Order-preserving (OP) interpolation operators, see
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2 % Almquist, Wang, Werpers,
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3 % "Order-Preserving Interpolation for Summation-by-Parts Operators
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4 % at Non-Conforming Interfaces", https://arxiv.org/abs/1806.01931
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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.good = Iv2u.bad^*
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9 % Iv2u.good = Iu2v.bad^*
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10 %
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11 % The .bad operators have the same order of accuracy as the operators
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12 % by Mattsson and Carpenter (MC) in InterpOpsMC, i.e. order p,
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13 % if the interior stencil is order 2p. The .good operators are
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14 % one order more accurate, i.e. order p+1.
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15 %
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16 % For PDEs of second order in space, the OP operators allow for the same
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17 % convergence rate as with conforming interfaces, which is an improvement
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18 % by one order compared what is possible with the MC operators.
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19 classdef InterpOpsOP < sbp.InterpOps
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20 properties
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22 % Structs of interpolation operators, fields .good and .bad
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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 = InterpOpsOP(m_u, m_v, order_u, order_v)
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32 assert(order_u == order_v,...
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33 'InterpOpsOP: 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.intOpOP_orders_2to2_ratio2to1;
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38 case 4
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39 intOpSet = @sbp.implementations.intOpOP_orders_4to4_ratio2to1;
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40 case 6
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41 intOpSet = @sbp.implementations.intOpOP_orders_6to6_ratio2to1;
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42 case 8
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43 intOpSet = @sbp.implementations.intOpOP_orders_8to8_ratio2to1;
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44 otherwise
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45 error('InterpOpsOP: 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, 1, 'C2F');
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55 [Iv2u.bad, Iu2v.good] = intOpSet(m_C, 1, 'F2C');
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56
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57 elseif (m_v-1)/(m_u-1) == 2
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58 % Block v is fine, u is coarse
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59 m_C = m_u;
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60 [Iu2v.good, Iv2u.bad] = intOpSet(m_C, 1, 'C2F');
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61 [Iu2v.bad, Iv2u.good] = intOpSet(m_C, 1, 'F2C');
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62 else
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63 error('InterpOpsOP: Interpolation operators for grid ratio %f have not yet been constructed', (m_u-1)/(m_v-1));
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64 end
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66 obj.Iu2v = Iu2v;
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67 obj.Iv2u = Iv2u;
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69 end
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71 function str = string(obj)
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72 str = [class(obj)];
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73 end
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75 end
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76 end