--- a/+scheme/Beam2d.m	Wed Jan 16 16:35:01 2019 +0100
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,349 +0,0 @@
-classdef Beam2d < scheme.Scheme
-    properties
-        grid
-        order % Order accuracy for the approximation
-
-        D % non-stabalized scheme operator
-        M % Derivative norm
-        alpha
-
-        H % Discrete norm
-        Hi
-        H_x, H_y % Norms in the x and y directions
-        Hx,Hy % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir.
-        Hi_x, Hi_y
-        Hix, Hiy
-        e_w, e_e, e_s, e_n
-        d1_w, d1_e, d1_s, d1_n
-        d2_w, d2_e, d2_s, d2_n
-        d3_w, d3_e, d3_s, d3_n
-        gamm_x, gamm_y
-        delt_x, delt_y
-    end
-
-    methods
-        function obj = Beam2d(m,lim,order,alpha,opsGen)
-            default_arg('alpha',1);
-            default_arg('opsGen',@sbp.Higher);
-
-            if ~isa(grid, 'grid.Cartesian') || grid.D() ~= 2
-                error('Grid must be 2d cartesian');
-            end
-
-            obj.grid = grid;
-            obj.alpha = alpha;
-            obj.order = order;
-
-            m_x = grid.m(1);
-            m_y = grid.m(2);
-
-            h = grid.scaling();
-            h_x = h(1);
-            h_y = h(2);
-
-            ops_x = opsGen(m_x,h_x,order);
-            ops_y = opsGen(m_y,h_y,order);
-
-            I_x = speye(m_x);
-            I_y = speye(m_y);
-
-            D4_x = sparse(ops_x.derivatives.D4);
-            H_x =  sparse(ops_x.norms.H);
-            Hi_x = sparse(ops_x.norms.HI);
-            e_l_x = sparse(ops_x.boundary.e_1);
-            e_r_x = sparse(ops_x.boundary.e_m);
-            d1_l_x = sparse(ops_x.boundary.S_1);
-            d1_r_x = sparse(ops_x.boundary.S_m);
-            d2_l_x  = sparse(ops_x.boundary.S2_1);
-            d2_r_x  = sparse(ops_x.boundary.S2_m);
-            d3_l_x  = sparse(ops_x.boundary.S3_1);
-            d3_r_x  = sparse(ops_x.boundary.S3_m);
-
-            D4_y = sparse(ops_y.derivatives.D4);
-            H_y =  sparse(ops_y.norms.H);
-            Hi_y = sparse(ops_y.norms.HI);
-            e_l_y = sparse(ops_y.boundary.e_1);
-            e_r_y = sparse(ops_y.boundary.e_m);
-            d1_l_y = sparse(ops_y.boundary.S_1);
-            d1_r_y = sparse(ops_y.boundary.S_m);
-            d2_l_y  = sparse(ops_y.boundary.S2_1);
-            d2_r_y  = sparse(ops_y.boundary.S2_m);
-            d3_l_y  = sparse(ops_y.boundary.S3_1);
-            d3_r_y  = sparse(ops_y.boundary.S3_m);
-
-
-            D4 = kr(D4_x, I_y) + kr(I_x, D4_y);
-
-            % Norms
-            obj.H = kr(H_x,H_y);
-            obj.Hx  = kr(H_x,I_x);
-            obj.Hy  = kr(I_x,H_y);
-            obj.Hix = kr(Hi_x,I_y);
-            obj.Hiy = kr(I_x,Hi_y);
-            obj.Hi = kr(Hi_x,Hi_y);
-
-            % Boundary operators
-            obj.e_w  = kr(e_l_x,I_y);
-            obj.e_e  = kr(e_r_x,I_y);
-            obj.e_s  = kr(I_x,e_l_y);
-            obj.e_n  = kr(I_x,e_r_y);
-            obj.d1_w = kr(d1_l_x,I_y);
-            obj.d1_e = kr(d1_r_x,I_y);
-            obj.d1_s = kr(I_x,d1_l_y);
-            obj.d1_n = kr(I_x,d1_r_y);
-            obj.d2_w = kr(d2_l_x,I_y);
-            obj.d2_e = kr(d2_r_x,I_y);
-            obj.d2_s = kr(I_x,d2_l_y);
-            obj.d2_n = kr(I_x,d2_r_y);
-            obj.d3_w = kr(d3_l_x,I_y);
-            obj.d3_e = kr(d3_r_x,I_y);
-            obj.d3_s = kr(I_x,d3_l_y);
-            obj.d3_n = kr(I_x,d3_r_y);
-
-            obj.D = alpha*D4;
-
-            obj.gamm_x = h_x*ops_x.borrowing.N.S2/2;
-            obj.delt_x = h_x^3*ops_x.borrowing.N.S3/2;
-
-            obj.gamm_y = h_y*ops_y.borrowing.N.S2/2;
-            obj.delt_y = h_y^3*ops_y.borrowing.N.S3/2;
-        end
-
-
-        % Closure functions return the opertors applied to the own doamin to close the boundary
-        % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
-        %       boundary            is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
-        %       type                is a string specifying the type of boundary condition if there are several.
-        %       data                is a function returning the data that should be applied at the boundary.
-        %       neighbour_scheme    is an instance of Scheme that should be interfaced to.
-        %       neighbour_boundary  is a string specifying which boundary to interface to.
-        function [closure, penalty_e,penalty_d] = boundary_condition(obj,boundary,type,data)
-            default_arg('type','dn');
-            default_arg('data',0);
-
-            [e, d1, d2, d3] = obj.getBoundaryOperator({'e', 'd1', 'd2', 'd3'}, boundary);
-            s = obj.getBoundarySign(boundary);
-            [gamm, delt] = obj.getBoundaryBorrowing(boundary);
-            halfnorm_inv = obj.getHalfnormInv(boundary);
-
-            switch type
-                % Dirichlet-neumann boundary condition
-                case {'dn'}
-                    alpha = obj.alpha;
-
-                    % tau1 < -alpha^2/gamma
-                    tuning = 1.1;
-
-                    tau1 = tuning * alpha/delt;
-                    tau4 = s*alpha;
-
-                    sig2 = tuning * alpha/gamm;
-                    sig3 = -s*alpha;
-
-                    tau = tau1*e+tau4*d3;
-                    sig = sig2*d1+sig3*d2;
-
-                    closure = halfnorm_inv*(tau*e' + sig*d1');
-
-                    pp_e = halfnorm_inv*tau;
-                    pp_d = halfnorm_inv*sig;
-                    switch class(data)
-                        case 'double'
-                            penalty_e = pp_e*data;
-                            penalty_d = pp_d*data;
-                        case 'function_handle'
-                            penalty_e = @(t)pp_e*data(t);
-                            penalty_d = @(t)pp_d*data(t);
-                        otherwise
-                            error('Wierd data argument!')
-                    end
-
-                % Unknown, boundary condition
-                otherwise
-                    error('No such boundary condition: type = %s',type);
-            end
-        end
-
-        function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary, type)
-            % u denotes the solution in the own domain
-            % v denotes the solution in the neighbour domain
-            [e_u, d1_u, d2_u, d3_u] = obj.getBoundaryOperator({'e', 'd1', 'd2', 'd3'}, boundary);
-            s_u = obj.getBoundarySign(boundary);
-            [gamm_u, delt_u] = obj.getBoundaryBorrowing(boundary);
-            halfnorm_inv = obj.getHalfnormInv(boundary);
-
-            [e_v, d1_v, d2_v, d3_v] = neighbour_scheme.getBoundaryOperator({'e', 'd1', 'd2', 'd3'}, neighbour_boundary);
-            s_v = neighbour_scheme.getBoundarySign(neighbour_boundary);
-            [gamm_v, delt_v] = neighbour_scheme.getBoundaryBorrowing(neighbour_boundary);
-
-            tuning = 2;
-
-            alpha_u = obj.alpha;
-            alpha_v = neighbour_scheme.alpha;
-
-            tau1 = ((alpha_u/2)/delt_u + (alpha_v/2)/delt_v)/2*tuning;
-            % tau1 = (alpha_u/2 + alpha_v/2)/(2*delt_u)*tuning;
-            tau4 = s_u*alpha_u/2;
-
-            sig2 = ((alpha_u/2)/gamm_u + (alpha_v/2)/gamm_v)/2*tuning;
-            sig3 = -s_u*alpha_u/2;
-
-            phi2 = s_u*1/2;
-
-            psi1 = -s_u*1/2;
-
-            tau = tau1*e_u  +                     tau4*d3_u;
-            sig =           sig2*d1_u + sig3*d2_u          ;
-            phi =           phi2*d1_u                      ;
-            psi = psi1*e_u                                 ;
-
-            closure =  halfnorm_inv*(tau*e_u' + sig*d1_u' + phi*alpha_u*d2_u' + psi*alpha_u*d3_u');
-            penalty = -halfnorm_inv*(tau*e_v' + sig*d1_v' + phi*alpha_v*d2_v' + psi*alpha_v*d3_v');
-        end
-
-        % Returns the boundary operator op for the boundary specified by the string boundary.
-        % op        -- string or a cell array of strings
-        % boundary  -- string
-        function varargout = getBoundaryOperator(obj, op, boundary)
-
-            if ~iscell(op)
-                op = {op};
-            end
-
-            for i = 1:numel(op)
-                switch op{i}
-                case 'e'
-                    switch boundary
-                    case 'w'
-                        e = obj.e_w;
-                    case 'e'
-                        e = obj.e_e;
-                    case 's'
-                        e = obj.e_s;
-                    case 'n'
-                        e = obj.e_n;
-                    otherwise
-                        error('No such boundary: boundary = %s',boundary);
-                    end
-                    varargout{i} = e;
-
-                case 'd1'
-                    switch boundary
-                    case 'w'
-                        d1 = obj.d1_w;
-                    case 'e'
-                        d1 = obj.d1_e;
-                    case 's'
-                        d1 = obj.d1_s;
-                    case 'n'
-                        d1 = obj.d1_n;
-                    otherwise
-                        error('No such boundary: boundary = %s',boundary);
-                    end
-                    varargout{i} = d1;
-                end
-
-                case 'd2'
-                    switch boundary
-                    case 'w'
-                        d2 = obj.d2_w;
-                    case 'e'
-                        d2 = obj.d2_e;
-                    case 's'
-                        d2 = obj.d2_s;
-                    case 'n'
-                        d2 = obj.d2_n;
-                    otherwise
-                        error('No such boundary: boundary = %s',boundary);
-                    end
-                    varargout{i} = d2;
-                end
-
-                case 'd3'
-                    switch boundary
-                    case 'w'
-                        d3 = obj.d3_w;
-                    case 'e'
-                        d3 = obj.d3_e;
-                    case 's'
-                        d3 = obj.d3_s;
-                    case 'n'
-                        d3 = obj.d3_n;
-                    otherwise
-                        error('No such boundary: boundary = %s',boundary);
-                    end
-                    varargout{i} = d3;
-                end
-            end
-        end
-
-        % Returns square boundary quadrature matrix, of dimension
-        % corresponding to the number of boundary points
-        %
-        % boundary -- string
-        function H_b = getBoundaryQuadrature(obj, boundary)
-
-            switch boundary
-                case 'w'
-                    H_b = obj.H_y;
-                case 'e'
-                    H_b = obj.H_y;
-                case 's'
-                    H_b = obj.H_x;
-                case 'n'
-                    H_b = obj.H_x;
-                otherwise
-                    error('No such boundary: boundary = %s',boundary);
-            end
-        end
-
-        % Returns the boundary sign. The right boundary is considered the positive boundary
-        % boundary -- string
-        function s = getBoundarySign(obj, boundary)
-            switch boundary
-                case {'e','n'}
-                    s = 1;
-                case {'w','s'}
-                    s = -1;
-                otherwise
-                    error('No such boundary: boundary = %s',boundary);
-            end
-        end
-
-        % Returns the halfnorm_inv used in SATs. TODO: better notation
-        function Hinv = getHalfnormInv(obj, boundary)
-            switch boundary
-                case 'w'
-                    Hinv = obj.Hix;
-                case 'e'
-                    Hinv = obj.Hix;
-                case 's'
-                    Hinv = obj.Hiy;
-                case 'n'
-                    Hinv = obj.Hiy;
-                otherwise
-                    error('No such boundary: boundary = %s',boundary);
-            end
-        end
-
-        % Returns borrowing constant gamma
-        % boundary -- string
-        function [gamm, delt] = getBoundaryBorrowing(obj, boundary)
-            switch boundary
-                case {'w','e'}
-                    gamm = obj.gamm_x;
-                    delt = obj.delt_x;
-                case {'s','n'}
-                    gamm = obj.gamm_y;
-                    delt = obj.delt_y;
-                otherwise
-                    error('No such boundary: boundary = %s',boundary);
-            end
-        end
-
-        function N = size(obj)
-            N = prod(obj.m);
-        end
-
-    end
-end