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view +sbp/+implementations/d1_noneq_minimal_4.m @ 1337:bf2554f1825d feature/D2_boundary_opt
Add periodic D1 and D2 operators for orders 8,10,12
author | Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
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date | Fri, 13 May 2022 13:28:10 +0200 |
parents | 4cb627c7fb90 |
children |
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function [D1,H] = d1_noneq_minimal_4(N,h) % N: Number of grid points if(N<6) error('Operator requires at least 6 grid points'); end % BP: Number of boundary points BP = 3; %%%% Norm matrix %%%%%%%% P = sparse(BP,1); %#ok<*NASGU> P0 = 2.6864248295847e-01; P1 = 1.0094667153500e+00; P2 = 9.9312068011715e-01; for i = 0:BP-1 P(i+1) = eval(['P' num2str(i)]); end H = ones(N,1); H(1:BP) = P; H(end-BP+1:end) = flip(P); H = spdiags(h*H,0,N,N); %%%%%%%%%%%%%%%%%%%%%%%%% %%%% Q matrix %%%%%%%%%%% % interior stencil order = 4; d = [1/12,-2/3,0,2/3,-1/12]; d = repmat(d,N,1); Q = spdiags(d,-order/2:order/2,N,N); % Boundaries Q0_0 = -5.0000000000000e-01; Q0_1 = 6.1697245625434e-01; Q0_2 = -1.1697245625434e-01; Q0_3 = 0.0000000000000e+00; Q0_4 = 0.0000000000000e+00; Q1_0 = -6.1697245625434e-01; Q1_1 = 0.0000000000000e+00; Q1_2 = 7.0030578958767e-01; Q1_3 = -8.3333333333333e-02; Q1_4 = 0.0000000000000e+00; Q2_0 = 1.1697245625434e-01; Q2_1 = -7.0030578958767e-01; Q2_2 = 0.0000000000000e+00; Q2_3 = 6.6666666666667e-01; Q2_4 = -8.3333333333333e-02; for i = 1:BP for j = 1:BP Q(i,j) = eval(['Q' num2str(i-1) '_' num2str(j-1)]); Q(N+1-i,N+1-j) = -eval(['Q' num2str(i-1) '_' num2str(j-1)]); end end %%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% Difference operator %% D1 = H\Q; %%%%%%%%%%%%%%%%%%%%%%%%%%%