--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/+grid/Schrodinger2dCurve.m	Thu Feb 09 11:41:21 2017 +0100
@@ -0,0 +1,290 @@
+classdef Schrodinger2dCurve < scheme.Scheme
+    properties
+        m % Number of points in each direction, possibly a vector
+        h % Grid spacing
+
+        grid
+
+        order % Order accuracy for the approximation
+
+        D % non-stabalized scheme operator
+        M % Derivative norm
+        H % Discrete norm
+        Hi
+        H_u, H_v % Norms in the x and y directions
+        Hu,Hv % Kroneckerd norms. 1'*Hx*v corresponds to integration in the x dir.
+        Hi_u, Hi_v
+        Hiu, Hiv
+        D1_v D1_u
+        D2_v D2_u
+        Du Dv
+        
+ 
+        e_w, e_e, e_s, e_n
+        du_w, dv_w
+        du_e, dv_e
+        du_s, dv_s
+        du_n, dv_n
+        g_1
+        g_2
+        
+        p,p_tau
+    end
+
+    methods
+        function obj = Schrodinger2dCurve(g ,order, opSet, p,p_tau)
+            default_arg('opSet',@sbp.D2Variable);
+            default_arg('c', 1);
+
+            assert(isa(g, 'grid.Curvilinear'))
+            
+            obj.p=p;
+            obj.p_tau=p_tau;
+            obj.c=1;
+            
+            m = g.size();
+            m_u = m(1);
+            m_v = m(2);
+            m_tot = g.N();
+
+            h = g.scaling();
+            h_u = h(1);
+            h_v = h(2);
+
+            % Operators
+            ops_u = opSet(m_u, {0, 1}, order);
+            ops_v = opSet(m_v, {0, 1}, order);
+
+            I_u = speye(m_u);
+            I_v = speye(m_v);
+
+            D1_u = ops_u.D1;
+           
+            H_u =  ops_u.H;
+            Hi_u = ops_u.HI;
+            e_l_u = ops_u.e_l;
+            e_r_u = ops_u.e_r;
+            d1_l_u = ops_u.d1_l;
+            d1_r_u = ops_u.d1_r;
+
+            obj.D1_v = ops_v.D1;
+            obj.D2_v = ops_v.D2;
+            H_v =  ops_v.H;
+            Hi_v = ops_v.HI;
+            e_l_v = ops_v.e_l;
+            e_r_v = ops_v.e_r;
+            d1_l_v = ops_v.d1_l;
+            d1_r_v = ops_v.d1_r;
+
+            obj.Du = kr(D1_u,I_v);
+            obj.Dv = kr(I_u,D1_v);
+
+            obj.H = kr(H_u,H_v);
+            obj.Hi = kr(Hi_u,Hi_v);
+            obj.Hu  = kr(H_u,I_v);
+            obj.Hv  = kr(I_u,H_v);
+            obj.Hiu = kr(Hi_u,I_v);
+            obj.Hiv = kr(I_u,Hi_v);
+
+            obj.e_w  = kr(e_l_u,I_v);
+            obj.e_e  = kr(e_r_u,I_v);
+            obj.e_s  = kr(I_u,e_l_v);
+            obj.e_n  = kr(I_u,e_r_v);
+            obj.du_w = kr(d1_l_u,I_v);
+            obj.dv_w = (obj.e_w'*Dv)';
+            obj.du_e = kr(d1_r_u,I_v);
+            obj.dv_e = (obj.e_e'*Dv)';
+            obj.du_s = (obj.e_s'*Du)';
+            obj.dv_s = kr(I_u,d1_l_v);
+            obj.du_n = (obj.e_n'*Du)';
+            obj.dv_n = kr(I_u,d1_r_v);
+
+%             obj.x_u = x_u;
+%             obj.x_v = x_v;
+%             obj.y_u = y_u;
+%             obj.y_v = y_v;
+
+            obj.m = m;
+            obj.h = [h_u h_v];
+            obj.order = order;
+            obj.grid = g;
+
+
+        end
+
+        
+        function [D ]= d_fun(obj,t)
+                        % Metric derivatives
+            ti = parametrization.Ti.points(obj.p.p1(t),obj.p.p2(t),obj.p.p3,obj.p.p4);
+            ti_tau = parametrization.Ti.points(obj.p_tau.p1(t),obj.p_tau.p2(t),obj.p_tau.p3,obj.p_tau.p4);
+            
+            coords = parametrization.ti.map();
+            coords_tau = parametrization.ti_tau.map();
+            x = coords(:,1);
+            y = coords(:,2);
+
+            x_tau = coords_tau(:,1);
+            y_tau = coords_tau(:,2); 
+            
+            x_u = obj.Du*x;
+            x_v = obj.Dv*x;
+            y_u = obj.Du*y;
+            y_v = obj.Dv*y;
+
+            J = x_u.*y_v - x_v.*y_u;
+            a11 =  1./J.* (x_v.^2  + y_v.^2);
+            a12 = -1./J .* (x_u.*x_v + y_u.*y_v);
+            a22 =  1./J .* (x_u.^2  + y_u.^2);
+            lambda = 1/2 * (a11 + a22 - sqrt((a11-a22).^2 + 4*a12.^2));
+
+            % Assemble full operators
+            L_12 = spdiags(a12, 0, m_tot, m_tot);
+            Duv = obj.Du*L_12*obj.Dv;
+            Dvu = obj.Dv*L_12*obj.Du;
+
+            Duu = sparse(m_tot);
+            Dvv = sparse(m_tot);
+            ind = grid.funcToMatrix(g, 1:m_tot);
+
+            for i = 1:m_v
+                D = D2_u(a11(ind(:,i)));
+                p = ind(:,i);
+                Duu(p,p) = D;
+            end
+
+            for i = 1:m_u
+                D = D2_v(a22(ind(i,:)));
+                p = ind(i,:);
+                Dvv(p,p) = D;
+            end
+         
+
+            J = spdiags(J, 0, m_tot, m_tot);
+            Ji = spdiags(1./J, 0, m_tot, m_tot);
+            obj.g_1 = x_tau.*y_v-y_tau.*x_v;
+            obj.g_2 = -x_tau.*y_u + y_tau.*x_u;
+            
+            %Add the flux splitting
+            D = Ji*(obj.g_1*obj.Du + obj.g_2*obj.Dv + 1i*obj.c^2*(Duu + Duv + Dvu + Dvv));
+            
+%             obj.gamm_u = h_u*ops_u.borrowing.M.d1;
+%             obj.gamm_v = h_v*ops_v.borrowing.M.d1;
+            
+        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, parameter)
+            default_arg('type','neumann');
+            default_arg('parameter', []);
+
+                    % v denotes the solution in the neighbour domain
+                    tuning = 1.2;
+                    % tuning = 20.2;
+                    [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv_n, halfnorm_inv_t, halfnorm_t,g] = obj.get_boundary_ops(boundary);
+
+                    a_n = spdiag(coeff_n);
+                    a_t = spdiag(coeff_t);
+
+                    F = (s * a_n * d_n' + s * a_t*d_t')';
+
+                    u = obj;
+
+                    b1 = gamm*u.lambda./u.a11.^2;
+                    b2 = gamm*u.lambda./u.a22.^2;
+
+                    tau1  = -1./b1 - 1./b2;
+                    tau1 = tuning * spdiag(tau1);
+                    sig1 = 1;
+                    
+                    a = e'*g;
+                    tau2 =  (-1*s*a - abs(a))/4;
+
+                    penalty_parameter_1 = halfnorm_inv_n*(tau1 + sig1*halfnorm_inv_t*F*e'*halfnorm_t)*e;
+                    penalty_parameter_2 = halfnorm_inv_n(tau2)*e;
+
+                    closure = obj.Ji*obj.c^2 * penalty_parameter_1*e' +obj.Ji* penalty_parameter_2*e';
+                    penalty = -obj.Ji*obj.c^2 * penalty_parameter_1;
+                
+        end
+
+        function [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv_n, halfnorm_inv_t, halfnorm_t, I, scale_factor,g] = get_boundary_ops(obj, boundary)
+
+            % gridMatrix = zeros(obj.m(2),obj.m(1));
+            % gridMatrix(:) = 1:numel(gridMatrix);
+
+            ind = grid.funcToMatrix(obj.grid, 1:prod(obj.m));
+
+            switch boundary
+                case 'w'
+                    e = obj.e_w;
+                    d_n = obj.du_w;
+                    d_t = obj.dv_w;
+                    s = -1;
+
+                    I = ind(1,:);
+                    coeff_n = obj.a11(I);
+                    coeff_t = obj.a12(I);
+                    scale_factor = sqrt(obj.x_v(I).^2 + obj.y_v(I).^2);
+                case 'e'
+                    e = obj.e_e;
+                    d_n = obj.du_e;
+                    d_t = obj.dv_e;
+                    s = 1;
+
+                    I = ind(end,:);
+                    coeff_n = obj.a11(I);
+                    coeff_t = obj.a12(I);
+                    scale_factor = sqrt(obj.x_v(I).^2 + obj.y_v(I).^2);
+                case 's'
+                    e = obj.e_s;
+                    d_n = obj.dv_s;
+                    d_t = obj.du_s;
+                    s = -1;
+
+                    I = ind(:,1)';
+                    coeff_n = obj.a22(I);
+                    coeff_t = obj.a12(I);
+                    scale_factor = sqrt(obj.x_u(I).^2 + obj.y_u(I).^2);
+                case 'n'
+                    e = obj.e_n;
+                    d_n = obj.dv_n;
+                    d_t = obj.du_n;
+                    s = 1;
+
+                    I = ind(:,end)';
+                    coeff_n = obj.a22(I);
+                    coeff_t = obj.a12(I);
+                    scale_factor = sqrt(obj.x_u(I).^2 + obj.y_u(I).^2);
+                otherwise
+                    error('No such boundary: boundary = %s',boundary);
+            end
+
+            switch boundary
+                case {'w','e'}
+                    halfnorm_inv_n = obj.Hiu;
+                    halfnorm_inv_t = obj.Hiv;
+                    halfnorm_t = obj.Hv;
+                    gamm = obj.gamm_u;
+                    g=obj.g_1;
+                case {'s','n'}
+                    halfnorm_inv_n = obj.Hiv;
+                    halfnorm_inv_t = obj.Hiu;
+                    halfnorm_t = obj.Hu;
+                    gamm = obj.gamm_v;
+                    g=obj.g_2;
+            end
+        end
+
+        function N = size(obj)
+            N = prod(obj.m);
+        end
+
+
+    end
+end
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