--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/+scheme/Wave2d.m	Thu Sep 17 10:12:50 2015 +0200
@@ -0,0 +1,231 @@
+classdef SchmWave2d < noname.Scheme
+    properties
+        m % Number of points in each direction, possibly a vector
+        h % Grid spacing
+        x,y % 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
+        gamm_x, gamm_y
+    end
+
+    methods
+        function obj = SchmWave2d(m,xlim,ylim,order,alpha)
+            default_arg('a',1);
+
+            if length(m) == 1
+                m = [m m];
+            end
+
+            m_x = m(1);
+            m_y = m(2);
+
+            [x, h_x] = util.get_grid(xlim{:},m_x);
+            [y, h_y] = util.get_grid(ylim{:},m_y);
+
+            ops_x = sbp.Ordinary(m_x,h_x,order);
+            ops_y = sbp.Ordinary(m_y,h_y,order);
+
+            I_x = speye(m_x);
+            I_y = speye(m_y);
+
+            D2_x = sparse(ops_x.derivatives.D2);
+            H_x =  sparse(ops_x.norms.H);
+            Hi_x = sparse(ops_x.norms.HI);
+            M_x =  sparse(ops_x.norms.M);
+            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_y = sparse(ops_y.derivatives.D2);
+            H_y =  sparse(ops_y.norms.H);
+            Hi_y = sparse(ops_y.norms.HI);
+            M_y =  sparse(ops_y.norms.M);
+            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 = kr(D2_x, I_y) + kr(I_x, D2_y);
+            obj.H = kr(H_x,H_y);
+            obj.Hx  = kr(H_x,I_y);
+            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);
+            obj.M = kr(M_x,H_y)+kr(H_x,M_y);
+            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.m = m;
+            obj.h = [h_x h_y];
+            obj.order = order;
+
+            obj.alpha = alpha;
+            obj.D = alpha*D2;
+            obj.x = x;
+            obj.y = 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.M.S;
+            obj.gamm_y = h_y*ops_y.borrowing.M.S;
+        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] = boundary_condition(obj,boundary,type,data)
+            default_arg('type','neumann');
+            default_arg('data',0);
+
+            [e,d,s,gamm,halfnorm_inv] = obj.get_boundary_ops(boundary);
+
+            switch type
+                % Dirichlet boundary condition
+                case {'D','d','dirichlet'}
+                    alpha = obj.alpha;
+
+                    % tau1 < -alpha^2/gamma
+                    tuning = 1.1;
+                    tau1 = -tuning*alpha/gamm;
+                    tau2 =  s*alpha;
+
+                    p = tau1*e + tau2*d;
+
+                    closure = halfnorm_inv*p*e';
+
+                    pp = halfnorm_inv*p;
+                    switch class(data)
+                        case 'double'
+                            penalty = pp*data;
+                        case 'function_handle'
+                            penalty = @(t)pp*data(t);
+                        otherwise
+                            error('Wierd data argument!')
+                    end
+
+
+                % Neumann boundary condition
+                case {'N','n','neumann'}
+                    alpha = obj.alpha;
+                    tau1 = -s*alpha;
+                    tau2 = 0;
+                    tau = tau1*e + tau2*d;
+
+                    closure = halfnorm_inv*tau*d';
+
+                    pp = halfnorm_inv*tau;
+                    switch class(data)
+                        case 'double'
+                            penalty = pp*data;
+                        case 'function_handle'
+                            penalty = @(t)pp*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,d_u,s_u,gamm_u, halfnorm_inv] = obj.get_boundary_ops(boundary);
+            [e_v,d_v,s_v,gamm_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
+
+            tuning = 1.1;
+
+            alpha_u = obj.alpha;
+            alpha_v = neighbour_scheme.alpha;
+
+            % tau1 < -(alpha_u/gamm_u + alpha_v/gamm_v)
+
+            tau1 = -(alpha_u/gamm_u + alpha_v/gamm_v) * tuning;
+            tau2 = s_u*1/2*alpha_u;
+            sig1 = s_u*(-1/2);
+            sig2 = 0;
+
+            tau = tau1*e_u + tau2*d_u;
+            sig = sig1*e_u + sig2*d_u;
+
+            closure = halfnorm_inv*( tau*e_u' + sig*alpha_u*d_u');
+            penalty = halfnorm_inv*(-tau*e_v' - sig*alpha_v*d_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,d,s,gamm, halfnorm_inv] = get_boundary_ops(obj,boundary)
+            switch boundary
+                case 'w'
+                    e = obj.e_w;
+                    d = obj.d1_w;
+                    s = -1;
+                    gamm = obj.gamm_x;
+                    halfnorm_inv = obj.Hix;
+                case 'e'
+                    e = obj.e_e;
+                    d = obj.d1_e;
+                    s = 1;
+                    gamm = obj.gamm_x;
+                    halfnorm_inv = obj.Hix;
+                case 's'
+                    e = obj.e_s;
+                    d = obj.d1_s;
+                    s = -1;
+                    gamm = obj.gamm_y;
+                    halfnorm_inv = obj.Hiy;
+                case 'n'
+                    e = obj.e_n;
+                    d = obj.d1_n;
+                    s = 1;
+                    gamm = obj.gamm_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
+
+    methods(Static)
+        % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u
+        % and bound_v of scheme schm_v.
+        %   [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l')
+        function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
+            [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
+            [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
+        end
+    end
+end
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