Mercurial > repos > public > sbplib
view +sbp/+implementations/d2_blocknorm_4.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 | f7ac3cd6eeaa |
children |
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function [H, HI, D1, D2, e_1, e_m, M, Q, S_1, S_m] = d2_blocknorm_4(m,h) BP = 4; if(m<2*BP) error(['Operator requires at least ' num2str(2*BP) ' grid points']); end H_U=[0.751e3 / 0.3456e4 0.661e3 / 0.3456e4 -0.515e3 / 0.3456e4 0.5e1 / 0.128e3; 0.661e3 / 0.3456e4 0.1405e4 / 0.1152e4 -0.3e1 / 0.128e3 0.29e2 / 0.3456e4; -0.515e3 / 0.3456e4 -0.3e1 / 0.128e3 0.989e3 / 0.1152e4 0.149e3 / 0.3456e4; 0.5e1 / 0.128e3 0.29e2 / 0.3456e4 0.149e3 / 0.3456e4 0.3407e4 / 0.3456e4;]; H=speye(m); H(1:4,1:4)=H_U; H(m-3:m,m-3:m)=rot90( H_U(1:4,1:4) ,2 ); H=H*h; HI=inv(H); e=ones(m,1); Q=spdiags([e -8*e 0*e 8*e -e], -2:2, m, m)/12; % Q=(-1/12*diag(ones(m-2,1),2)+8/12*diag(ones(m-1,1),1)-8/12*diag(ones(m-1,1),-1)+1/12*diag(ones(m-2,1),-2)); Q_U = [-0.1e1 / 0.2e1 0.55e2 / 0.72e2 -0.47e2 / 0.144e3 0.1e1 / 0.16e2; -0.55e2 / 0.72e2 0 0.43e2 / 0.48e2 -0.19e2 / 0.144e3; 0.47e2 / 0.144e3 -0.43e2 / 0.48e2 0 0.47e2 / 0.72e2; -0.1e1 / 0.16e2 0.19e2 / 0.144e3 -0.47e2 / 0.72e2 0;]; Q(1:4,1:4)=Q_U; Q(m-3:m,m-3:m)=rot90( -Q_U(1:4,1:4) ,2 ); D1=H\Q; M_U=[0.359e3 / 0.288e3 -0.443e3 / 0.288e3 0.97e2 / 0.288e3 -0.13e2 / 0.288e3; -0.51e2 / 0.32e2 0.325e3 / 0.96e2 -0.191e3 / 0.96e2 0.19e2 / 0.96e2; 0.43e2 / 0.96e2 -0.69e2 / 0.32e2 0.293e3 / 0.96e2 -0.137e3 / 0.96e2; -0.29e2 / 0.288e3 0.89e2 / 0.288e3 -0.427e3 / 0.288e3 0.727e3 / 0.288e3;]; % M=-(-1/12*diag(ones(m-2,1),2)+16/12*diag(ones(m-1,1),1)+16/12*diag(ones(m-1,1),-1)-1/12*diag(ones(m-2,1),-2)-30/12*diag(ones(m,1),0)); M=-spdiags([-e 16*e -30*e 16*e -e], -2:2, m, m)/12; M(1:4,1:4)=M_U; M(m-3:m,m-3:m)=rot90( M_U ,2 ); M=M/h; DS_U=[0.25e2 / 0.12e2 -4 3 -0.4e1 / 0.3e1 0.1e1 / 0.4e1;]; DS=sparse(m,m); DS(1,1:5)=DS_U; DS(m,m-4:m)=fliplr(DS_U); DS=DS/h; D2=H\(-M+DS); % d3=[-1 3 -3 1]; % t3=sum(abs(d3)); % DD_3(1:1,1:4)=[d3]; % DD_3(m:m,m-3:m)=[d3]; % This works for wave eq. % For studs interface in 1D no AD is needed. % ADD=1*h/(t3)*DD_3'*DD_3; e_1 = sparse(m,1); e_1(1)= 1; e_m = sparse(m,1); e_m(end)= 1; S_1 = -DS(1,:)'; S_m = DS(end,:)'; Q = H*D1-(-(e_1*e_1') + (e_m*e_m')); M = -(H*D2-(-e_1*S_1' + e_m*S_m')); end