diff +sbp/InterpOpsMC.m @ 1033:037f203b9bf5 feature/burgers1d

Merge with branch feature/advectioRV to utilize the +rv package
author Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date Thu, 17 Jan 2019 10:44:12 +0100
parents 27ce3f653aa7
children
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--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/+sbp/InterpOpsMC.m	Thu Jan 17 10:44:12 2019 +0100
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+% Interpolation operators by Mattsson and Carpenter (MC), see
+% Mattsson and Carpenter,
+% "Stable and Accurate Interpolatino Operators for High-Order Multiblock Finite DIfference Methods",
+% https://epubs.siam.org/doi/pdf/10.1137/090750068
+%
+% Let ^* denote the adjoint. These operators satsify
+%
+% Iuv2 = Iv2u^*
+%
+% Both Iu2v and Iv2u have p:th order accuracy, if the interior stencil is
+% of order 2p.
+%
+% This approach leads to a reduction of the convergence rate by one order for
+% PDEs with 2nd derivatives in space, as compared to conforming interfaces.
+% To obtain full convergence rate, use the order-preserving (OP) operators in
+% InterpOpsOP.m
+classdef InterpOpsMC < sbp.InterpOps
+    properties
+
+        % Structs of interpolation operators, fields .good and .bad
+        % Here .good and .bad are the same, but this makes them fit in the
+        % OP (order-preserving) framework.
+        Iu2v
+        Iv2u
+    end
+
+    methods
+        % m_u, m_v         --   number of grid points along the interface
+        % order_u, order_v --   order of accuracy in the different blocks
+        function obj = InterpOpsMC(m_u, m_v, order_u, order_v)
+
+            assert(order_u == order_v,...
+                    'InterpOpsMC: Different orders of accuracy not available');
+
+            switch order_u
+            case 2
+                intOpSet = @sbp.implementations.intOpMC_orders_2to2_ratio2to1;
+            case 4
+                intOpSet = @sbp.implementations.intOpMC_orders_4to4_ratio2to1;
+            case 6
+                intOpSet = @sbp.implementations.intOpMC_orders_6to6_ratio2to1;
+            case 8
+                intOpSet = @sbp.implementations.intOpMC_orders_8to8_ratio2to1;
+            otherwise
+                error('InterpOpsMC: Order of accuracy %d not available.', order_u);
+            end
+
+            Iu2v = struct;
+            Iv2u = struct;
+
+            if (m_u-1)/(m_v-1) == 2
+                % Block u is fine, v is coarse
+                m_C = m_v;
+                [Iv2u.good, Iu2v.bad] = intOpSet(m_C);
+                Iv2u.bad = Iv2u.good;
+                Iu2v.good = Iu2v.bad;
+
+            elseif (m_v-1)/(m_u-1) == 2
+                % Block v is fine, u is coarse
+                m_C = m_u;
+                [Iu2v.good, Iv2u.bad] = intOpSet(m_C);
+                Iu2v.bad = Iu2v.good;
+                Iv2u.good = Iv2u.bad;
+            else
+                error('InterpOpsMC: Interpolation operators for grid ratio %f have not yet been constructed', (m_u-1)/(m_v-1));
+            end
+
+            obj.Iu2v = Iu2v;
+            obj.Iv2u = Iv2u;
+
+        end
+
+        function str = string(obj)
+            str = [class(obj)];
+        end
+
+    end
+end