Mercurial > repos > public > sbplib
view +sbp/+implementations/d4_lonely_4_min_boundary_points.m @ 1198:2924b3a9b921 feature/d2_compatible
Add OpSet for fully compatible D2Variable, created from regular D2Variable by replacing d1 by first row of D1. Formal reduction by one order of accuracy at the boundary point.
author | Martin Almquist <malmquist@stanford.edu> |
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date | Fri, 16 Aug 2019 14:30:28 -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