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view +sbp/+implementations/d4_lonely_8_min_boundary_points.m @ 1322:412b8ceafbc6 feature/poroelastic

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Add Zt to output args for Elastic2dCurvilinearAnisotropic.interfaceNormalTangential
author Martin Almquist <malmquist@stanford.edu>
date Sat, 24 Oct 2020 20:58:26 -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_8_min_boundary_points(m,h)
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    %%% 8:te ordn. SBP Finita differens         %%%
    %%% operatorer med diagonal norm            %%%
    %%%                                         %%%
    %%%                                         %%%
    %%% 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                            %%%
    %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    BP = 8;
    if(m<2*BP)
        error(['Operator requires at least ' num2str(2*BP) ' grid points']);
    end

    % Norm
    Hv = ones(m,1);
    Hv(1:8) = [1498139/5080320, 1107307/725760, 20761/80640, 1304999/725760, 299527/725760, 103097/80640, 670091/725760, 5127739/5080320];
    Hv(m-7:m) = rot90(Hv(1:8),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(1:6) = [-0.137e3/0.60e2 5 -5 0.10e2/0.3e1 -0.5e1/0.4e1 0.1e1/0.5e1;]/h;
    d1_r = -rot90(d1_l, 2);

    d2_l = sparse(m,1);
    d2_l(1:6) = [0.15e2/0.4e1 -0.77e2/0.6e1 0.107e3/0.6e1 -13 0.61e2/0.12e2 -0.5e1/0.6e1;]/h^2;
    d2_r = rot90(d2_l, 2);

    d3_l = sparse(m,1);
    d3_l(1:6) = [-0.17e2/0.4e1 0.71e2/0.4e1 -0.59e2/0.2e1 0.49e2/0.2e1 -0.41e2/0.4e1 0.7e1/0.4e1;]/h^3;
    d3_r = -rot90(d3_l, 2);


    % Fourth derivative, 1th order accurate at first 8 boundary points

    stencil = [-0.41e2/0.7560e4, 0.1261e4/0.15120e5,-0.541e3/0.840e3,0.4369e4/0.1260e4,-0.1669e4/0.180e3,0.1529e4/0.120e3,-0.1669e4/0.180e3,0.4369e4/0.1260e4,-0.541e3/0.840e3, 0.1261e4/0.15120e5,-0.41e2/0.7560e4];
    diags = -5:5;
    M4 = stripeMatrix(stencil, diags, m);

    M4_U = [
        0.151705142321e12/0.29189160000e11 -0.25643455801727e14/0.1634592960000e13 0.286417898677e12/0.15135120000e11 -0.4038072020317e13/0.326918592000e12 0.96455968907e11/0.20432412000e11 -0.151076916769e12/0.181621440000e12 0.14511526363e11/0.408648240000e12 -0.196663079e9/0.33359040000e11;
         -0.25643455801727e14/0.1634592960000e13 0.735383382473e12/0.14594580000e11 -0.5035391734409e13/0.77837760000e11 0.20392440917e11/0.467026560e9 -0.109540902413e12/0.6671808000e10 0.2488686539e10/0.884520000e9 -0.2798067539e10/0.33359040000e11 0.6433463591e10/0.408648240000e12;
         0.286417898677e12/0.15135120000e11 -0.5035391734409e13/0.77837760000e11 0.145019791981e12/0.1621620000e10 -0.333577111061e12/0.5189184000e10 0.18928722391e11/0.778377600e9 -0.93081704557e11/0.25945920000e11 -0.372660319e9/0.3243240000e10 0.2861399869e10/0.544864320000e12;
         -0.4038072020317e13/0.326918592000e12 0.20392440917e11/0.467026560e9 -0.333577111061e12/0.5189184000e10 0.59368471277e11/0.1167566400e10 -0.201168708569e12/0.9340531200e10 0.1492314487e10/0.432432000e9 0.1911896257e10/0.9340531200e10 0.24383341e8/0.2554051500e10;
         0.96455968907e11/0.20432412000e11 -0.109540902413e12/0.6671808000e10 0.18928722391e11/0.778377600e9 -0.201168708569e12/0.9340531200e10 0.1451230301e10/0.106142400e9 -0.103548247007e12/0.15567552000e11 0.27808437809e11/0.11675664000e11 -0.36870830713e11/0.65383718400e11;
         -0.151076916769e12/0.181621440000e12 0.2488686539e10/0.884520000e9 -0.93081704557e11/0.25945920000e11 0.1492314487e10/0.432432000e9 -0.103548247007e12/0.15567552000e11 0.1229498243e10/0.115830000e9 -0.32222519717e11/0.3706560000e10 0.470092704233e12/0.136216080000e12;
         0.14511526363e11/0.408648240000e12 -0.2798067539e10/0.33359040000e11 -0.372660319e9/0.3243240000e10 0.1911896257e10/0.9340531200e10 0.27808437809e11/0.11675664000e11 -0.32222519717e11/0.3706560000e10 0.11547819313e11/0.912161250e9 -0.15187033999199e14/0.1634592960000e13;
         -0.196663079e9/0.33359040000e11 0.6433463591e10/0.408648240000e12 0.2861399869e10/0.544864320000e12 0.24383341e8/0.2554051500e10 -0.36870830713e11/0.65383718400e11 0.470092704233e12/0.136216080000e12 -0.15187033999199e14/0.1634592960000e13 0.33832994693e11/0.2653560000e10;
    ];

    M4(1:8,1:8) = M4_U;
    M4(m-7:m,m-7: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