--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/+scheme/Beam2d.m	Thu Sep 17 10:12:50 2015 +0200
@@ -0,0 +1,259 @@
+classdef SchmBeam2d < noname.Scheme
+    properties
+        m % Number of points in each direction, possibly a vector
+        N % Number of points total
+        h % Grid spacing
+        u,v % Grid
+        x,y % Values of x and y for each grid point
+        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 = SchmBeam2d(m,lim,order,alpha,opsGen)
+            default_arg('opsGen',@sbp.Higher);
+            default_arg('a',1);
+
+            if length(m) == 1
+                m = [m m];
+            end
+
+            m_x = m(1);
+            m_y = m(2);
+
+            xlim = lim{1};
+            ylim = lim{2};
+
+            [x, h_x] = util.get_grid(xlim{:},m_x);
+            [y, h_y] = util.get_grid(ylim{:},m_y);
+
+            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.m = m;
+            obj.h = [h_x h_y];
+            obj.order = order;
+
+            obj.alpha = alpha;
+            obj.D = alpha*D4;
+            obj.u = x;
+            obj.v = y;
+            obj.x = kr(x,ones(m_y,1));
+            obj.y = kr(ones(m_x,1),y);
+
+            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,s,gamm,delt,halfnorm_inv] = obj.get_boundary_ops(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)
+            % u denotes the solution in the own domain
+            % v denotes the solution in the neighbour domain
+            [e_u,d1_u,d2_u,d3_u,s_u,gamm_u,delt_u, halfnorm_inv] = obj.get_boundary_ops(boundary);
+            [e_v,d1_v,d2_v,d3_v,s_v,gamm_v,delt_v] = neighbour_scheme.get_boundary_ops(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
+
+        % Ruturns the boundary ops and sign for the boundary specified by the string boundary.
+        % The right boundary is considered the positive boundary
+        function [e,d1,d2,d3,s,gamm, delt, halfnorm_inv] = get_boundary_ops(obj,boundary)
+            switch boundary
+                case 'w'
+                    e  = obj.e_w;
+                    d1 = obj.d1_w;
+                    d2 = obj.d2_w;
+                    d3 = obj.d3_w;
+                    s = -1;
+                    gamm = obj.gamm_x;
+                    delt = obj.delt_x;
+                    halfnorm_inv = obj.Hix;
+                case 'e'
+                    e  = obj.e_e;
+                    d1 = obj.d1_e;
+                    d2 = obj.d2_e;
+                    d3 = obj.d3_e;
+                    s = 1;
+                    gamm = obj.gamm_x;
+                    delt = obj.delt_x;
+                    halfnorm_inv = obj.Hix;
+                case 's'
+                    e  = obj.e_s;
+                    d1 = obj.d1_s;
+                    d2 = obj.d2_s;
+                    d3 = obj.d3_s;
+                    s = -1;
+                    gamm = obj.gamm_y;
+                    delt = obj.delt_y;
+                    halfnorm_inv = obj.Hiy;
+                case 'n'
+                    e  = obj.e_n;
+                    d1 = obj.d1_n;
+                    d2 = obj.d2_n;
+                    d3 = obj.d3_n;
+                    s = 1;
+                    gamm = obj.gamm_y;
+                    delt = obj.delt_y;
+                    halfnorm_inv = obj.Hiy;
+                otherwise
+                    error('No such boundary: boundary = %s',boundary);
+            end
+        end
+
+        function N = size(obj)
+            N = prod(obj.m);
+        end
+
+    end
+end