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comparison +sbp/InterpOpsOP.m @ 979:7a5e770974ed feature/timesteppers

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Merge with default
author Jonatan Werpers <jonatan@werpers.com>
date Mon, 07 Jan 2019 16:26:00 +0100
parents 27ce3f653aa7
children
comparison
equal deleted inserted replaced
933:34b3d092a4d0 979:7a5e770974ed
1 % Order-preserving (OP) interpolation operators, see
2 % Almquist, Wang, Werpers,
3 % "Order-Preserving Interpolation for Summation-by-Parts Operators
4 % at Non-Conforming Interfaces", https://arxiv.org/abs/1806.01931
5 %
6 % Let ^* denote the adjoint. These operators satsify
7 %
8 % Iuv2.good = Iv2u.bad^*
9 % Iv2u.good = Iu2v.bad^*
10 %
11 % The .bad operators have the same order of accuracy as the operators
12 % by Mattsson and Carpenter (MC) in InterpOpsMC, i.e. order p,
13 % if the interior stencil is order 2p. The .good operators are
14 % one order more accurate, i.e. order p+1.
15 %
16 % For PDEs of second order in space, the OP operators allow for the same
17 % convergence rate as with conforming interfaces, which is an improvement
18 % by one order compared what is possible with the MC operators.
19 classdef InterpOpsOP < sbp.InterpOps
20 properties
21
22 % Structs of interpolation operators, fields .good and .bad
23 Iu2v
24 Iv2u
25 end
26
27 methods
28 % m_u, m_v -- number of grid points along the interface
29 % order_u, order_v -- order of accuracy in the different blocks
30 function obj = InterpOpsOP(m_u, m_v, order_u, order_v)
31
32 assert(order_u == order_v,...
33 'InterpOpsOP: Different orders of accuracy not available');
34
35 switch order_u
36 case 2
37 intOpSet = @sbp.implementations.intOpOP_orders_2to2_ratio2to1;
38 case 4
39 intOpSet = @sbp.implementations.intOpOP_orders_4to4_ratio2to1;
40 case 6
41 intOpSet = @sbp.implementations.intOpOP_orders_6to6_ratio2to1;
42 case 8
43 intOpSet = @sbp.implementations.intOpOP_orders_8to8_ratio2to1;
44 otherwise
45 error('InterpOpsOP: Order of accuracy %d not available.', order_u);
46 end
47
48 Iu2v = struct;
49 Iv2u = struct;
50
51 if (m_u-1)/(m_v-1) == 2
52 % Block u is fine, v is coarse
53 m_C = m_v;
54 [Iv2u.good, Iu2v.bad] = intOpSet(m_C, 1, 'C2F');
55 [Iv2u.bad, Iu2v.good] = intOpSet(m_C, 1, 'F2C');
56
57 elseif (m_v-1)/(m_u-1) == 2
58 % Block v is fine, u is coarse
59 m_C = m_u;
60 [Iu2v.good, Iv2u.bad] = intOpSet(m_C, 1, 'C2F');
61 [Iu2v.bad, Iv2u.good] = intOpSet(m_C, 1, 'F2C');
62 else
63 error('InterpOpsOP: Interpolation operators for grid ratio %f have not yet been constructed', (m_u-1)/(m_v-1));
64 end
65
66 obj.Iu2v = Iu2v;
67 obj.Iv2u = Iv2u;
68
69 end
70
71 function str = string(obj)
72 str = [class(obj)];
73 end
74
75 end
76 end