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view +sbp/D2Standard.m @ 1198:2924b3a9b921 feature/d2_compatible

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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>
date Fri, 16 Aug 2019 14:30:28 -0700
parents bc78157c89cb
children eca4ca84cf0a
line wrap: on
line source

classdef D2Standard < sbp.OpSet
    properties
        D1 % SBP operator approximating first derivative
        H % Norm matrix
        HI % H^-1
        Q % Skew-symmetric matrix
        e_l % Left boundary operator
        e_r % Right boundary operator
        D2 % SBP operator for second derivative
        M % Norm matrix, second derivative
        d1_l % Left boundary first derivative
        d1_r % Right boundary first derivative
        m % Number of grid points.
        h % Step size
        x % grid
        borrowing % Struct with borrowing limits for different norm matrices

    end

    methods
        function obj = D2Standard(m,lim,order)

            x_l = lim{1};
            x_r = lim{2};
            L = x_r-x_l;
            obj.h = L/(m-1);
            obj.x = linspace(x_l,x_r,m)';

            if order == 2
                [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
                obj.e_r, obj.M, obj.Q, obj.d1_l, obj.d1_r] =...
                sbp.implementations.d2_2(m,obj.h);
                obj.borrowing.M.S = 0.4000;
            elseif order == 4
                [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
                obj.e_r, obj.M, obj.Q, obj.d1_l, obj.d1_r] =...
                sbp.implementations.d2_4(m,obj.h);
                obj.borrowing.M.S = 0.2508;
            elseif order == 6
                [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
                obj.e_r, obj.M, obj.Q, obj.d1_l, obj.d1_r] =...
                sbp.implementations.d2_6(m,obj.h);
                obj.borrowing.M.S = 0.1878;
            elseif order == 8
                [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
                obj.e_r, obj.M, obj.Q, obj.d1_l, obj.d1_r] =...
                sbp.implementations.d2_8(m,obj.h);
                obj.borrowing.M.S = 0.0015;
            elseif order == 10
                [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
                obj.e_r, obj.M, obj.Q, obj.d1_l, obj.d1_r] =...
                sbp.implementations.d2_10(m,obj.h);
                obj.borrowing.M.S = 0.0351;
            elseif order == 12
                [obj.H, obj.HI, obj.D1, obj.D2, obj.e_l,...
                obj.e_r, obj.M, obj.Q, obj.d1_l, obj.d1_r] =...
                sbp.implementations.d2_12(m,obj.h);
                obj.borrowing.M.S = []; % Need to compute!
                warning('D2=D1*D1 (wide stencil).');
                warning('The borrowing constant has not been computed.')
            else
                error('Invalid operator order %d.',order);
            end

            obj.m = m;
        end

        function str = string(obj)
            str = [class(obj) '_' num2str(obj.order)];
        end

    end
end