view +sbp/+implementations/d4_lonely_6_min_boundary_points.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 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_6_min_boundary_points(m,h)
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %%% 6:te ordn. SBP Finita differens         %%%
    %%% operatorer med diagonal norm            %%%
    %%% Extension to variable koeff             %%%
    %%%                                         %%%
    %%% H           (Normen)                    %%%
    %%% D1=H^(-1)Q  (approx f?rsta derivatan)   %%%
    %%% D2          (approx andra derivatan)    %%%
    %%% D2=HI*(R+C*D*S                          %%%
    %%%                                         %%%
    %%% R=-D1'*H*C*D1-RR                        %%%
    %%%                                         %%%
    %%% RR ?r dissipation)                      %%%
    %%% Dissipationen uppbyggd av D4:           %%%
    %%% DI=D4*B*H*D4                            %%%
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    % H?r med 6 RP ist?llet f?r 8 f?r D4 operatorn, dock samma randderivator

    BP = 6;
    if(m<2*BP)
        error(['Operator requires at least ' num2str(2*BP) ' grid points']);
    end

    % Norm
    Hv = ones(m,1);
    Hv(1:6) = [13649/43200,12013/8640,2711/4320,5359/4320,7877/8640, 43801/43200];
    Hv(m-5:m) = rot90(Hv(1:6),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(1:5) = [-25/12, 4, -3, 4/3, -1/4]/h;
    d1_r = -rot90(d1_l, 2);

    d2_l = sparse(m,1);
    d2_l(1:5) = [0.35e2/0.12e2 -0.26e2/0.3e1 0.19e2/0.2e1 -0.14e2/0.3e1 0.11e2/0.12e2;]/h^2;
    d2_r = rot90(d2_l, 2);

    d3_l = sparse(m,1);
    d3_l(1:5) = [-0.5e1/0.2e1 9 -12 7 -0.3e1/0.2e1;]/h^3;
    d3_r = -rot90(d3_l, 2);


    % Fourth derivative, 1th order accurate at first 8 boundary points (still
    % yield 5th order convergence if stable: for example u_tt=-u_xxxx

    stencil = [7/240, -2/5, 169/60, -122/15, 91/8, -122/15, 169/60, -2/5, 7/240];
    diags = -4:4;
    M4 = stripeMatrix(stencil, diags, m);

    M4_U=[
        0.3504379e7/0.907200e6 -0.4613983e7/0.453600e6 0.4260437e7/0.453600e6 -0.418577e6/0.113400e6 0.524579e6/0.907200e6 0.535e3/0.18144e5;
        -0.4613983e7/0.453600e6 0.5186159e7/0.181440e6 -0.81121e5/0.2835e4 0.218845e6/0.18144e5 -0.159169e6/0.90720e5 -0.94669e5/0.907200e6;
        0.4260437e7/0.453600e6 -0.81121e5/0.2835e4 0.147695e6/0.4536e4 -0.384457e6/0.22680e5 0.339653e6/0.90720e5 -0.18233e5/0.113400e6;
        -0.418577e6/0.113400e6 0.218845e6/0.18144e5 -0.384457e6/0.22680e5 0.65207e5/0.4536e4 -0.22762e5/0.2835e4 0.1181753e7/0.453600e6;
        0.524579e6/0.907200e6 -0.159169e6/0.90720e5 0.339653e6/0.90720e5 -0.22762e5/0.2835e4 0.2006171e7/0.181440e6 -0.3647647e7/0.453600e6;
        0.535e3/0.18144e5 -0.94669e5/0.907200e6 -0.18233e5/0.113400e6 0.1181753e7/0.453600e6 -0.3647647e7/0.453600e6 0.10305271e8/0.907200e6;
    ];

    M4(1:6,1:6) = M4_U;
    M4(m-5:m,m-5: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