Mercurial > repos > public > sbplib
view +sbp/+implementations/d4_lonely_4_min_boundary_points.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_4_min_boundary_points(m,h) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%% 4:de ordn. SBP Finita differens %%% %%% operatorer framtagna av Mark Carpenter %%% %%% %%% %%% H (Normen) %%% %%% D1=H^(-1)Q (approx f?rsta derivatan) %%% %%% D2 (approx andra derivatan) %%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %H?r med endast 4 randpunkter BP = 4; if(m<2*BP) error(['Operator requires at least ' num2str(2*BP) ' grid points']); end % Norm Hv = ones(m,1); Hv(1:4) = [17/48 59/48 43/48 49/48]; Hv(m-3:m) = rot90(Hv(1:4),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(1:4) = 1/h*[-11/6 3 -3/2 1/3]; d1_r = -rot90(d1_l, 2); d2_l = sparse(m,1); d2_l(1:4) = 1/h^2*[2 -5 4 -1]; d2_r = rot90(d2_l, 2); d3_l = sparse(m,1); d3_l(1:4) = 1/h^3*[-1 3 -3 1]; d3_r = -rot90(d3_l, 2); % First derivative stencil = [1/12 -2/3 0 2/3 -1/12]; diags = [-1 0 1]; Q_U = [ 0 0.59e2/0.96e2 -0.1e1/0.12e2 -0.1e1/0.32e2; -0.59e2/0.96e2 0 0.59e2/0.96e2 0; 0.1e1/0.12e2 -0.59e2/0.96e2 0 0.59e2/0.96e2; 0.1e1/0.32e2 0 -0.59e2/0.96e2 0; ]; Q = stripeMatrix(stencil, diags, m); Q(1:4,1:4)=Q_U; Q(m-3:m,m-3:m) = -rot90(Q_U, 2); D1 = HI*(Q - 1/2*e_l*e_l' + 1/2*e_r*e_r'); % Fourth derivative stencil = [-1/6, 2, -13/2, 28/3, -13/2, 2, -1/6]; diags = -3:3; M4 = stripeMatrix(stencil, diags, m); M4_U=[ 0.8e1/0.3e1 -0.37e2/0.6e1 0.13e2/0.3e1 -0.5e1/0.6e1; -0.37e2/0.6e1 0.47e2/0.3e1 -13 0.11e2/0.3e1; 0.13e2/0.3e1 -13 0.44e2/0.3e1 -0.47e2/0.6e1; -0.5e1/0.6e1 0.11e2/0.3e1 -0.47e2/0.6e1 0.29e2/0.3e1; ]; M4(1:4,1:4) = M4_U; M4(m-3:m,m-3: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