Mercurial > repos > public > sbplib
view +sbp/+implementations/d4_lonely_6_2.m @ 1330:855871e0b852 feature/D2_boundary_opt
Add size checks to the operators
author | Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
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date | Thu, 17 Feb 2022 18:55:11 +0100 |
parents | b19e142fcae1 |
children |
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function [H, HI, D4, e_l, e_r, M4, d2_l, d2_r, d3_l, d3_r, d1_l, d1_r] = d4_variable_6_2(m,h) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% 6:te ordn. SBP Finita differens %%% %%% operatorer med diagonal norm %%% %%% Extension to variable koeff %%% %%% %%% %%% H (Normen) %%% %%% D1=H^(-1)Q (approx f?rsta derivatan) %%% %%% D2 (approx andra derivatan) %%% %%% D2=HI*(R+C*D*S %%% %%% %%% %%% R=-D1'*H*C*D1-RR %%% %%% %%% %%% RR ?r dissipation) %%% %%% Dissipationen uppbyggd av D4: %%% %%% DI=D4*B*H*D4 %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % H?r med 6 RP ist?llet f?r 8 f?r D4 operatorn, dock samma randderivator % Denna ?r noggrannare, och har 2a ordningens randdslutning och b?r ge 6te % ordningens konvergens. Hade dock ingen fri parameter att optimera BP = 6; if(m<2*BP) error(['Operator requires at least ' num2str(2*BP) ' grid points']); end % Norm Hv = ones(m,1); Hv(1:6) = [0.181e3/0.576e3, 0.1343e4/0.960e3, 0.293e3/0.480e3, 0.1811e4/0.1440e4, 0.289e3/0.320e3, 0.65e2/0.64e2]; Hv(m-5:m) = rot90(Hv(1:6),2); Hv = h*Hv; H = spdiag(Hv, 0); HI = spdiag(1./Hv, 0); % Boundary operators e_l = sparse(m,1); e_l(1) = 1; e_r = rot90(e_l, 2); d1_l = sparse(m,1); d1_l(1:6) = [-0.137e3/0.60e2 5 -5 0.10e2/0.3e1 -0.5e1/0.4e1 0.1e1/0.5e1;]/h; d1_r = -rot90(d1_l, 2); d2_l = sparse(m,1); d2_l(1:6) = [0.15e2/0.4e1 -0.77e2/0.6e1 0.107e3/0.6e1 -13 0.61e2/0.12e2 -0.5e1/0.6e1;]/h^2; d2_r = rot90(d2_l, 2); d3_l = sparse(m,1); d3_l(1:6) = [-0.17e2/0.4e1 0.71e2/0.4e1 -0.59e2/0.2e1 0.49e2/0.2e1 -0.41e2/0.4e1 0.7e1/0.4e1;]/h^3; d3_r = -rot90(d3_l, 2); % Fourth derivative, 1th order accurate at first 8 boundary points (still % yield 5th order convergence if stable: for example u_tt = -u_xxxx stencil = [7/240, -2/5, 169/60, -122/15, 91/8, -122/15, 169/60, -2/5, 7/240]; diags = -4:4; M4 = stripeMatrix(stencil, diags, m); M4_U = [ 0.1009e4/0.192e3 -0.7657e4/0.480e3 0.9307e4/0.480e3 -0.509e3/0.40e2 0.4621e4/0.960e3 -0.25e2/0.32e2; -0.7657e4/0.480e3 0.49513e5/0.960e3 -0.4007e4/0.60e2 0.21799e5/0.480e3 -0.8171e4/0.480e3 0.2657e4/0.960e3; 0.9307e4/0.480e3 -0.4007e4/0.60e2 0.1399e4/0.15e2 -0.2721e4/0.40e2 0.12703e5/0.480e3 -0.521e3/0.120e3; -0.509e3/0.40e2 0.21799e5/0.480e3 -0.2721e4/0.40e2 0.3349e4/0.60e2 -0.389e3/0.15e2 0.559e3/0.96e2; 0.4621e4/0.960e3 -0.8171e4/0.480e3 0.12703e5/0.480e3 -0.389e3/0.15e2 0.17857e5/0.960e3 -0.1499e4/0.160e3; -0.25e2/0.32e2 0.2657e4/0.960e3 -0.521e3/0.120e3 0.559e3/0.96e2 -0.1499e4/0.160e3 0.2225e4/0.192e3; ]; M4(1:6,1:6) = M4_U; M4(m-5:m,m-5:m) = rot90(M4_U, 2); M4 = 1/h^3*M4; D4=HI*(M4 - e_l*d3_l'+e_r*d3_r' + d1_l*d2_l'-d1_r*d2_r'); end