Mercurial > repos > public > sbplib
view +sbp/+implementations/d4_variable_6_min_boundary_points.m @ 324:c0cbffcf6513 feature/beams
Created new operator class for lonely D4 operators. Removed some output parameters of implementations.
author | Jonatan Werpers <jonatan@werpers.com> |
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date | Mon, 26 Sep 2016 09:51:45 +0200 |
parents | fc91e3a2d44a |
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_min_boundary_points(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 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) = [13649/43200,12013/8640,2711/4320,5359/4320,7877/8640, 43801/43200]; 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(1:5) = [-25/12, 4, -3, 4/3, -1/4]/h; d1_r = -rot90(d1_l); d2_l = sparse(m,1); d2_l(1:5) = [0.35e2/0.12e2 -0.26e2/0.3e1 0.19e2/0.2e1 -0.14e2/0.3e1 0.11e2/0.12e2;]/h^2; d2_r = rot90(d2_l, 2); d3_l = sparse(m,1); d3_l(1:5) = [-0.5e1/0.2e1 9 -12 7 -0.3e1/0.2e1;]/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=[ 0.3504379e7/0.907200e6 -0.4613983e7/0.453600e6 0.4260437e7/0.453600e6 -0.418577e6/0.113400e6 0.524579e6/0.907200e6 0.535e3/0.18144e5; -0.4613983e7/0.453600e6 0.5186159e7/0.181440e6 -0.81121e5/0.2835e4 0.218845e6/0.18144e5 -0.159169e6/0.90720e5 -0.94669e5/0.907200e6; 0.4260437e7/0.453600e6 -0.81121e5/0.2835e4 0.147695e6/0.4536e4 -0.384457e6/0.22680e5 0.339653e6/0.90720e5 -0.18233e5/0.113400e6; -0.418577e6/0.113400e6 0.218845e6/0.18144e5 -0.384457e6/0.22680e5 0.65207e5/0.4536e4 -0.22762e5/0.2835e4 0.1181753e7/0.453600e6; 0.524579e6/0.907200e6 -0.159169e6/0.90720e5 0.339653e6/0.90720e5 -0.22762e5/0.2835e4 0.2006171e7/0.181440e6 -0.3647647e7/0.453600e6; 0.535e3/0.18144e5 -0.94669e5/0.907200e6 -0.18233e5/0.113400e6 0.1181753e7/0.453600e6 -0.3647647e7/0.453600e6 0.10305271e8/0.907200e6; ]; 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