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view +sbp/+implementations/d2_variable_periodic_8.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 |
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function [H, HI, D1, D2, e_l, e_r, d1_l, d1_r] = d2_variable_periodic_8(m,h) % m = number of unique grid points, i.e. h = L/m; if(m<9) error(['Operator requires at least ' num2str(8) ' grid points']); end % Norm Hv = ones(m,1); Hv = h*Hv; H = spdiag(Hv, 0); HI = spdiag(1./Hv, 0); % Dummy boundary operators e_l = sparse(m,1); e_r = rot90(e_l, 2); d1_l = sparse(m,1); d1_r = -rot90(d1_l, 2); % D1 operator diags = -4:4; stencil = [1/280, -4/105, 1/5, -4/5, 0, 4/5, -1/5, 4/105, -1/280]; D1 = stripeMatrixPeriodic(stencil, diags, m); D1 = D1/h; % Undivided differences diags = -3:2; stencil = [-1 5 -10 10 -5 1]; DD_5 = stripeMatrixPeriodic(stencil, diags, m); diags = -3:3; stencil = [1 -6 15 -20 15 -6 1]; DD_6 = stripeMatrixPeriodic(stencil, diags, m); diags = -4:3; stencil = [-1 7 -21 35 -35 21 -7 1]; DD_7 = stripeMatrixPeriodic(stencil, diags, m); diags = -4:4; stencil = [1 -8 28 -56 70 -56 28 -8 1]; DD_8 = stripeMatrixPeriodic(stencil, diags, m); % D2 operator function D2 = D2_fun(c) C1 = sparse(diag(c)); diags = -1:0; stencil = [1/2, 1/2]; C2 = stripeMatrixPeriodic(stencil, diags, m); diags = -1:1; stencil = [3/10, 2/5, 3/10]; C3 = stripeMatrixPeriodic(stencil, diags, m); diags = -2:1; stencil = [1/4, 1/4, 1/4, 1/4]; C4 = stripeMatrixPeriodic(stencil, diags, m); C2 = sparse(diag(C2 * c)); C3 = sparse(diag(C3 * c)); C4 = sparse(diag(C4 * c)); % Remainder term added to wide second derivative operator R = (1/78400 / h) * transpose(DD_8) * C1 * DD_8 + (1/14700 / h) * transpose(DD_7) * C2 * DD_7 + (1/2520 / h) * transpose(DD_6) * C3 * DD_6 + (1/350 / h) * transpose(DD_5) * C4 * DD_5; D2 = D1 * C1 * D1 - H \ R; end D2 = @D2_fun; end