Mercurial > repos > public > sbplib
view +sbp/+implementations/d4_lonely_4_min_boundary_points.m @ 577:e45c9b56d50d feature/grids
Add an Empty grid class
The need turned up for the flexural code when we may or may not have a grid for the open water and want to plot that solution.
In case there is no open water we need an empty grid to plot the empty gridfunction against to avoid errors.
author | Jonatan Werpers <jonatan@werpers.com> |
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date | Thu, 07 Sep 2017 09:16:12 +0200 |
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