Mercurial > repos > public > sbplib
view +sbp/+implementations/d4_lonely_4_min_boundary_points.m @ 774:66eb4a2bbb72 feature/grids
Remove default scaling of the system.
The scaling doens't seem to help actual solutions. One example that fails in the flexural code.
With large timesteps the solutions seems to blow up. One particular example is profilePresentation
on the tdb_presentation_figures branch with k = 0.0005
author | Jonatan Werpers <jonatan@werpers.com> |
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date | Wed, 18 Jul 2018 15:42:52 -0700 |
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