view +sbp/+implementations/d1_upwind_4.m @ 958:72cd29107a9a feature/poroelastic

Temporary changes in multiblock.DiffOp. Change traction operators in Elastic2dvariable to be true boundary operators. But adjoint FD conv test fails for dirichlet BC so need to debug!
author Martin Almquist <malmquist@stanford.edu>
date Wed, 05 Dec 2018 18:58:10 -0800
parents 88584b0cfba1
children
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function [H, HI, Dp, Dm, e_1, e_m] = d1_upwind_4(m,h)

    if(m<8)
        error('Operator requires at least 8 grid points');
    end

    Hv=ones(m,1);
    Hv(1:4)=[49/144 61/48 41/48 149/144];
    Hv(m-3:m)=rot90(Hv(1:4),2);
    Hv = Hv*h;
    H = spdiag(Hv,0);
    HI = spdiag(1./Hv,0);

    q_diags   = [-1, 0, 1, 2 3];
    q_stencil = [-1/4 -5/6 3/2 -1/2 1/12];
    Qp = stripeMatrix(q_stencil, q_diags,m);

    Q_U = [
        -0.1e1/0.48e2    0.205e3/0.288e3 -0.29e2/0.144e3 0.1e1/0.96e2;
        -0.169e3/0.288e3 -0.11e2/0.48e2  0.33e2/0.32e2   -0.43e2/0.144e3;
        0.11e2/0.144e3   -0.13e2/0.32e2  -0.29e2/0.48e2  0.389e3/0.288e3;
        0.1e1/0.32e2     -0.11e2/0.144e3 -0.65e2/0.288e3 -0.13e2/0.16e2;
    ];

    Qp(1:4,1:4)=Q_U;
    Qp(m-3:m,m-3:m)=rot90(Q_U, 2)'; %%% This is different from standard SBP

    Qm=-Qp';

    e_1=sparse(m,1);e_1(1)=1;
    e_m=sparse(m,1);e_m(m)=1;

    Dp=HI*(Qp-1/2*(e_1*e_1')+1/2*(e_m*e_m')) ;

    Dm=HI*(Qm-1/2*(e_1*e_1')+1/2*(e_m*e_m')) ;
end