--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/+scheme/Elastic2dStaggeredAnisotropic.m	Wed Apr 29 21:05:01 2020 -0700
@@ -0,0 +1,809 @@
+classdef Elastic2dStaggeredAnisotropic < scheme.Scheme
+
+% Discretizes the elastic wave equation:
+% rho u_{i,tt} = dj C_{ijkl} dk u_j
+% Uses a staggered Lebedev grid
+% The solution (displacement) is stored on g_u
+% Stresses (and hance tractions) appear on g_s
+% Density is evaluated on g_u
+% The stiffness tensor is evaluated on g_s
+
+    properties
+        m % Number of points in each direction, possibly a vector
+        h % Grid spacing
+
+        grid
+        dim
+        nGrids
+        N       % Total number of unknowns stored (2 displacement components on 2 grids)
+
+        order % Order of accuracy for the approximation
+
+        % Diagonal matrices for variable coefficients
+        RHO  % Density
+        C    % Elastic stiffness tensor
+
+        D  % Total operator
+
+        % Boundary operators in cell format, used for BC
+        % T_w, T_e, T_s, T_n
+
+        % Traction operators
+        tau_w, tau_e, tau_s, tau_n      % Return scalar field
+
+        % Inner products
+        H, H_u, H_s
+        % , Hi, Hi_kron, H_1D
+
+        % Boundary inner products (for scalar field)
+        H_w_u, H_e_u, H_s_u, H_n_u
+        H_w_s, H_e_s, H_s_s, H_n_s
+
+        % Boundary restriction operators
+        e_w_u, e_e_u, e_s_u, e_n_u      % Act on scalar field, return scalar field at boundary
+        e_w_s, e_e_s, e_s_s, e_n_s      % Act on scalar field, return scalar field at boundary
+
+        % U{i}^T picks out component i
+        U
+
+        % G{i}^T picks out displacement grid i
+        G
+
+        % Borrowing constants of the form gamma*h, where gamma is a dimensionless constant.
+        h11 % First entry in norm matrix
+
+    end
+
+    methods
+
+        % The coefficients can either be function handles or grid functions
+        function obj = Elastic2dStaggeredAnisotropic(g, order, rho, C)
+            default_arg('rho', @(x,y) 0*x+1);
+            dim = 2;
+            nGrids = 2;
+
+            C_default = cell(dim,dim,dim,dim);
+            for i = 1:dim
+                for j = 1:dim
+                    for k = 1:dim
+                        for l = 1:dim
+                            C_default{i,j,k,l} = @(x,y) 0*x + 1;
+                        end
+                    end
+                end
+            end
+            default_arg('C', C_default);
+            assert(isa(g, 'grid.Staggered'))
+
+            g_u = g.gridGroups{1};
+            g_s = g.gridGroups{2};
+
+            m_u = {g_u{1}.size(), g_u{2}.size()};
+            m_s = {g_s{1}.size(), g_s{2}.size()};
+
+            if isa(rho, 'function_handle')
+                rho_vec = cell(nGrids, 1);
+                for i = 1:nGrids
+                    rho_vec{i} = grid.evalOn(g_u{i}, rho);
+                end
+                rho = rho_vec;
+            end
+            for i = 1:nGrids
+                RHO{i} = spdiag(rho{i});
+            end
+            obj.RHO = RHO;
+
+            C_mat = cell(nGrids, 1);
+            for a = 1:nGrids
+                C_mat{a} = cell(dim,dim,dim,dim);
+            end
+            for a = 1:nGrids
+                for i = 1:dim
+                    for j = 1:dim
+                        for k = 1:dim
+                            for l = 1:dim
+                                C_mat{a}{i,j,k,l} = spdiag(grid.evalOn(g_s{a}, C{i,j,k,l}));
+                            end
+                        end
+                    end
+                end
+            end
+            C = C_mat;
+            obj.C = C;
+
+            % Reference m for primal grid
+            m = g_u{1}.size();
+            X = g_u{1}.points;
+            lim = cell(dim, 1);
+            for i = 1:dim
+                lim{i} = {min(X(:,i)), max(X(:,i))};
+            end
+
+            % 1D operators
+            ops = cell(dim,1);
+            D1p = cell(dim, 1);
+            D1d = cell(dim, 1);
+            mp = cell(dim, 1);
+            md = cell(dim, 1);
+            Ip = cell(dim, 1);
+            Id = cell(dim, 1);
+            Hp = cell(dim, 1);
+            Hd = cell(dim, 1);
+
+            opSet = @sbp.D1StaggeredUpwind;
+            for i = 1:dim
+                ops{i} = opSet(m(i), lim{i}, order);
+                D1p{i} = ops{i}.D1_dual;
+                D1d{i} = ops{i}.D1_primal;
+                mp{i} = length(ops{i}.x_primal);
+                md{i} = length(ops{i}.x_dual);
+                Ip{i} = speye(mp{i}, mp{i});
+                Id{i} = speye(md{i}, md{i});
+                Hp{i} = ops{i}.H_primal;
+                Hd{i} = ops{i}.H_dual;
+                ep_l{i} = ops{i}.e_primal_l;
+                ep_r{i} = ops{i}.e_primal_r;
+                ed_l{i} = ops{i}.e_dual_l;
+                ed_r{i} = ops{i}.e_dual_r;
+            end
+
+            % Borrowing constants
+            for i = 1:dim
+                obj.h11{i} = ops{i}.H_dual(1,1);
+            end
+
+            %---- Grid layout -------
+            % gu1 = xp o yp;
+            % gu2 = xd o yd;
+            % gs1 = xd o yp;
+            % gs2 = xp o yd;
+            %------------------------
+
+            % Quadratures
+            obj.H_u = cell(nGrids, 1);
+            obj.H_s = cell(nGrids, 1);
+            obj.H_u{1} = kron(Hp{1}, Hp{2});
+            obj.H_u{2} = kron(Hd{1}, Hd{2});
+            obj.H_s{1} = kron(Hd{1}, Hp{2});
+            obj.H_s{2} = kron(Hp{1}, Hd{2});
+
+            obj.H_w_s = cell(nGrids, 1);
+            obj.H_e_s = cell(nGrids, 1);
+            obj.H_s_s = cell(nGrids, 1);
+            obj.H_n_s = cell(nGrids, 1);
+
+            obj.H_w_s{1} = Hp{2};
+            obj.H_w_s{2} = Hd{2};
+            obj.H_e_s{1} = Hp{2};
+            obj.H_e_s{2} = Hd{2};
+
+            obj.H_s_s{1} = Hd{1};
+            obj.H_s_s{2} = Hp{1};
+            obj.H_n_s{1} = Hd{1};
+            obj.H_n_s{2} = Hp{1};
+
+            % Boundary restriction ops
+            e_w_u = cell(nGrids, 1);
+            e_s_u = cell(nGrids, 1);
+            e_e_u = cell(nGrids, 1);
+            e_n_u = cell(nGrids, 1);
+
+            e_w_s = cell(nGrids, 1);
+            e_s_s = cell(nGrids, 1);
+            e_e_s = cell(nGrids, 1);
+            e_n_s = cell(nGrids, 1);
+
+            e_w_u{1} = kron(ep_l{1}, Ip{2});
+            e_e_u{1} = kron(ep_r{1}, Ip{2});
+            e_s_u{1} = kron(Ip{1}, ep_l{2});
+            e_n_u{1} = kron(Ip{1}, ep_r{2});
+
+            e_w_u{2} = kron(ed_l{1}, Id{2});
+            e_e_u{2} = kron(ed_r{1}, Id{2});
+            e_s_u{2} = kron(Id{1}, ed_l{2});
+            e_n_u{2} = kron(Id{1}, ed_r{2});
+
+            e_w_s{1} = kron(ed_l{1}, Ip{2});
+            e_e_s{1} = kron(ed_r{1}, Ip{2});
+            e_s_s{1} = kron(Id{1}, ep_l{2});
+            e_n_s{1} = kron(Id{1}, ep_r{2});
+
+            e_w_s{2} = kron(ep_l{1}, Id{2});
+            e_e_s{2} = kron(ep_r{1}, Id{2});
+            e_s_s{2} = kron(Ip{1}, ed_l{2});
+            e_n_s{2} = kron(Ip{1}, ed_r{2});
+
+            obj.e_w_u = e_w_u;
+            obj.e_e_u = e_e_u;
+            obj.e_s_u = e_s_u;
+            obj.e_n_u = e_n_u;
+
+            obj.e_w_s = e_w_s;
+            obj.e_e_s = e_e_s;
+            obj.e_s_s = e_s_s;
+            obj.e_n_s = e_n_s;
+
+
+            % D1_u2s{a, b}{i} approximates ddi and
+            %takes from u grid number b to s grid number a
+            % Some of D1_x2y{a, b} are 0.
+            D1_u2s = cell(nGrids, nGrids);
+            D1_s2u = cell(nGrids, nGrids);
+
+            N_u = cell(nGrids, 1);
+            N_s = cell(nGrids, 1);
+            for a = 1:nGrids
+                N_u{a} = g_u{a}.N();
+                N_s{a} = g_s{a}.N();
+            end
+
+            %---- Grid layout -------
+            % gu1 = xp o yp;
+            % gu2 = xd o yd;
+            % gs1 = xd o yp;
+            % gs2 = xp o yd;
+            %------------------------
+
+            D1_u2s{1,1}{1} = kron(D1p{1}, Ip{2});
+            D1_s2u{1,1}{1} = kron(D1d{1}, Ip{2});
+
+            D1_u2s{1,2}{2} = kron(Id{1}, D1d{2});
+            D1_u2s{2,1}{2} = kron(Ip{1}, D1p{2});
+
+            D1_s2u{1,2}{2} = kron(Ip{1}, D1d{2});
+            D1_s2u{2,1}{2} = kron(Id{1}, D1p{2});
+
+            D1_u2s{2,2}{1} = kron(D1d{1}, Id{2});
+            D1_s2u{2,2}{1} = kron(D1p{1}, Id{2});
+
+            D1_u2s{1,1}{2} = sparse(N_s{1}, N_u{1});
+            D1_s2u{1,1}{2} = sparse(N_u{1}, N_s{1});
+
+            D1_u2s{2,2}{2} = sparse(N_s{2}, N_u{2});
+            D1_s2u{2,2}{2} = sparse(N_u{2}, N_s{2});
+
+            D1_u2s{1,2}{1} = sparse(N_s{1}, N_u{2});
+            D1_s2u{1,2}{1} = sparse(N_u{1}, N_s{2});
+
+            D1_u2s{2,1}{1} = sparse(N_s{2}, N_u{1});
+            D1_s2u{2,1}{1} = sparse(N_u{2}, N_s{1});
+
+
+            %---- Combine grids and components -----
+
+            % U{a}{i}^T picks out u component i on grid a
+            U = cell(nGrids, 1);
+            for a = 1:2
+                U{a} = cell(dim, 1);
+                I = speye(N_u{a}, N_u{a});
+                for i = 1:dim
+                    E = sparse(dim,1);
+                    E(i) = 1;
+                    U{a}{i} = kron(I, E);
+                end
+            end
+            obj.U = U;
+
+            % Order grids
+            % u1, u2
+            Iu1 = speye(dim*N_u{1}, dim*N_u{1});
+            Iu2 = speye(dim*N_u{2}, dim*N_u{2});
+
+            Gu1 = cell2mat( {Iu1; sparse(dim*N_u{2}, dim*N_u{1})} );
+            Gu2 = cell2mat( {sparse(dim*N_u{1}, dim*N_u{2}); Iu2} );
+            G = {Gu1; Gu2};
+            obj.G = G;
+
+            obj.H = G{1}*(U{1}{1}*obj.H_u{1}*U{1}{1}' + U{1}{2}*obj.H_u{1}*U{1}{2}')*G{1}'...
+                  + G{2}*(U{2}{1}*obj.H_u{2}*U{2}{1}' + U{2}{2}*obj.H_u{2}*U{2}{2}')*G{2}';
+
+            % e1_w = (e_scalar_w'*E{1}')';
+            % e1_e = (e_scalar_e'*E{1}')';
+            % e1_s = (e_scalar_s'*E{1}')';
+            % e1_n = (e_scalar_n'*E{1}')';
+
+            % e2_w = (e_scalar_w'*E{2}')';
+            % e2_e = (e_scalar_e'*E{2}')';
+            % e2_s = (e_scalar_s'*E{2}')';
+            % e2_n = (e_scalar_n'*E{2}')';
+
+            % Differentiation matrix D (without SAT)
+            N = dim*(N_u{1} + N_u{2});
+            D = sparse(N, N);
+            for a = 1:nGrids
+                for b = 1:nGrids
+                    for c = 1:nGrids
+                        for i = 1:dim
+                            for j = 1:dim
+                                for k = 1:dim
+                                    for l = 1:dim
+                                        D = D + (G{a}*U{a}{j})*(RHO{a}\(D1_s2u{a,b}{i}*C{b}{i,j,k,l}*D1_u2s{b,c}{k}*U{c}{l}'*G{c}'));
+                                    end
+                                end
+                            end
+                        end
+                    end
+                end
+            end
+            obj.D = D;
+            clear D;
+            obj.N = N;
+            %=========================================%'
+
+            % Numerical traction operators for BC.
+            %
+            % Formula at boundary j: % tau^{j}_i = sum_l T^{j}_{il} u_l
+            %
+
+            n_w = obj.getNormal('w');
+            n_e = obj.getNormal('e');
+            n_s = obj.getNormal('s');
+            n_n = obj.getNormal('n');
+
+            tau_w = cell(nGrids, 1);
+            tau_e = cell(nGrids, 1);
+            tau_s = cell(nGrids, 1);
+            tau_n = cell(nGrids, 1);
+
+            for b = 1:nGrids
+                tau_w{b} = cell(dim, 1);
+                tau_e{b} = cell(dim, 1);
+                tau_s{b} = cell(dim, 1);
+                tau_n{b} = cell(dim, 1);
+                
+                for j = 1:dim
+                    tau_w{b}{j} = sparse(N, m_s{b}(2));
+                    tau_e{b}{j} = sparse(N, m_s{b}(2));
+                    tau_s{b}{j} = sparse(N, m_s{b}(1));
+                    tau_n{b}{j} = sparse(N, m_s{b}(1));
+                end
+
+                for c = 1:nGrids
+                    for i = 1:dim
+                        for j = 1:dim
+                            for k = 1:dim
+                                for l = 1:dim
+                                    sigma_b_ij = C{b}{i,j,k,l}*D1_u2s{b,c}{k}*U{c}{l}'*G{c}';
+
+                                    tau_w{b}{j} = tau_w{b}{j} + (e_w_s{b}'*n_w(i)*sigma_b_ij)';
+                                    tau_e{b}{j} = tau_e{b}{j} + (e_e_s{b}'*n_e(i)*sigma_b_ij)';
+                                    tau_s{b}{j} = tau_s{b}{j} + (e_s_s{b}'*n_s(i)*sigma_b_ij)';
+                                    tau_n{b}{j} = tau_n{b}{j} + (e_n_s{b}'*n_n(i)*sigma_b_ij)';
+                                end
+                            end
+                        end
+                    end
+                end
+            end
+
+            obj.tau_w = tau_w;
+            obj.tau_e = tau_e;
+            obj.tau_s = tau_s;
+            obj.tau_n = tau_n;
+
+            % D1 = obj.D1;
+
+            % Traction tensors, T_ij
+            % obj.T_w = T_l{1};
+            % obj.T_e = T_r{1};
+            % obj.T_s = T_l{2};
+            % obj.T_n = T_r{2};
+
+            % Restriction operators
+            % obj.e_w = e_w;
+            % obj.e_e = e_e;
+            % obj.e_s = e_s;
+            % obj.e_n = e_n;
+
+            % obj.e1_w = e1_w;
+            % obj.e1_e = e1_e;
+            % obj.e1_s = e1_s;
+            % obj.e1_n = e1_n;
+
+            % obj.e2_w = e2_w;
+            % obj.e2_e = e2_e;
+            % obj.e2_s = e2_s;
+            % obj.e2_n = e2_n;
+
+            % obj.e_scalar_w = e_scalar_w;
+            % obj.e_scalar_e = e_scalar_e;
+            % obj.e_scalar_s = e_scalar_s;
+            % obj.e_scalar_n = e_scalar_n;
+
+            % % First component of traction
+            % obj.tau1_w = tau_l{1}{1};
+            % obj.tau1_e = tau_r{1}{1};
+            % obj.tau1_s = tau_l{2}{1};
+            % obj.tau1_n = tau_r{2}{1};
+
+            % % Second component of traction
+            % obj.tau2_w = tau_l{1}{2};
+            % obj.tau2_e = tau_r{1}{2};
+            % obj.tau2_s = tau_l{2}{2};
+            % obj.tau2_n = tau_r{2}{2};
+
+            % % Traction vectors
+            % obj.tau_w = (e_w'*e1_w*obj.tau1_w')' + (e_w'*e2_w*obj.tau2_w')';
+            % obj.tau_e = (e_e'*e1_e*obj.tau1_e')' + (e_e'*e2_e*obj.tau2_e')';
+            % obj.tau_s = (e_s'*e1_s*obj.tau1_s')' + (e_s'*e2_s*obj.tau2_s')';
+            % obj.tau_n = (e_n'*e1_n*obj.tau1_n')' + (e_n'*e2_n*obj.tau2_n')';
+
+            % Misc.
+            obj.m = m;
+            obj.h = [];
+            obj.order = order;
+            obj.grid = g;
+            obj.dim = dim;
+            obj.nGrids = nGrids;
+
+        end
+
+
+        % Closure functions return the operators applied to the own domain to close the boundary
+        % Penalty functions return the operators 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'.
+        %       bc                  is a cell array of component and bc type, e.g. {1, 'd'} for Dirichlet condition
+        %                           on the first component. Can also be e.g.
+        %                           {'normal', 'd'} or {'tangential', 't'} for conditions on
+        %                           tangential/normal component.
+        %       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.
+
+        % For displacement bc:
+        % bc = {comp, 'd', dComps},
+        % where
+        % dComps = vector of components with displacement BC. Default: 1:dim.
+        % In this way, we can specify one BC at a time even though the SATs depend on all BC.
+        function [closure, penalty] = boundary_condition(obj, boundary, bc, tuning)
+            default_arg('tuning', 1.0);
+
+            assert( iscell(bc), 'The BC type must be a 2x1 or 3x1 cell array' );
+            comp = bc{1};
+            type = bc{2};
+            if ischar(comp)
+                comp = obj.getComponent(comp, boundary);
+            end
+
+            e       = obj.getBoundaryOperatorForScalarField('e_u', boundary);
+            tau     = obj.getBoundaryOperator('tau', boundary);
+            % T       = obj.getBoundaryTractionOperator(boundary);
+            % h11     = obj.getBorrowing(boundary);
+            H_gamma = obj.getBoundaryQuadratureForScalarField(boundary);
+            nu      = obj.getNormal(boundary);
+
+            U = obj.U;
+            G = obj.G;
+            H = obj.H_u;
+            RHO = obj.RHO;
+            C = obj.C;
+
+            switch boundary
+            case {'s', 'n'}
+                e = rot90(e,2);
+                G = rot90(G,2);
+                U = rot90(U,2);
+                H = rot90(H,2);
+                RHO = rot90(RHO,2);
+            end
+
+            dim = obj.dim;
+            nGrids = obj.nGrids;
+
+            m_tot = obj.N;
+
+            % Preallocate
+            [~, col] = size(tau{1}{1});
+            closure = sparse(m_tot, m_tot);
+%             penalty = sparse(m_tot, col);
+            penalty = cell(nGrids, 1);
+
+            j = comp;
+            switch type
+
+            % Dirichlet boundary condition
+            case {'D','d','dirichlet','Dirichlet','displacement','Displacement'}
+                error('not implemented');
+
+                if numel(bc) >= 3
+                    dComps = bc{3};
+                else
+                    dComps = 1:dim;
+                end
+
+                % Loops over components that Dirichlet penalties end up on
+                % Y: symmetrizing part of penalty
+                % Z: symmetric part of penalty
+                % X = Y + Z.
+
+                % Nonsymmetric part goes on all components to
+                % yield traction in discrete energy rate
+                for i = 1:dim
+                    Y = T{j,i}';
+                    X = e*Y;
+                    closure = closure + E{i}*RHOi*Hi*X'*e*H_gamma*(e'*E{j}' );
+                    penalty = penalty - E{i}*RHOi*Hi*X'*e*H_gamma;
+                end
+
+                % Symmetric part only required on components with displacement BC.
+                % (Otherwise it's not symmetric.)
+                for i = dComps
+                    Z = sparse(m_tot, m_tot);
+                    for l = 1:dim
+                        for k = 1:dim
+                            Z = Z + nu(l)*C{l,i,k,j}*nu(k);
+                        end
+                    end
+                    Z = -tuning*dim/h11*Z;
+                    X = Z;
+                    closure = closure + E{i}*RHOi*Hi*X'*e*H_gamma*(e'*E{j}' );
+                    penalty = penalty - E{i}*RHOi*Hi*X'*e*H_gamma;
+                end
+
+            % Free boundary condition
+            case {'F','f','Free','free','traction','Traction','t','T'}
+                for a = 1:nGrids
+                    closure = closure - G{a}*U{a}{j}*(RHO{a}\(H{a}\(e{a}*H_gamma{a}*tau{a}{j}')));
+                    penalty{a} = G{a}*U{a}{j}*(RHO{a}\(H{a}\(e{a}*H_gamma{a})));
+                end
+
+            % Unknown boundary condition
+            otherwise
+                error('No such boundary condition: type = %s',type);
+            end
+        end
+
+        % type     Struct that specifies the interface coupling.
+        %          Fields:
+        %          -- tuning:           penalty strength, defaults to 1.0
+        %          -- interpolation:    type of interpolation, default 'none'
+        function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary,type)
+
+            defaultType.tuning = 1.0;
+            defaultType.interpolation = 'none';
+            default_struct('type', defaultType);
+
+            switch type.interpolation
+            case {'none', ''}
+                [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type);
+            case {'op','OP'}
+                [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type);
+            otherwise
+                error('Unknown type of interpolation: %s ', type.interpolation);
+            end
+        end
+
+        function [closure, penalty] = interfaceStandard(obj,boundary,neighbour_scheme,neighbour_boundary,type)
+            tuning = type.tuning;
+
+            % u denotes the solution in the own domain
+            % v denotes the solution in the neighbour domain
+
+            u = obj;
+            v = neighbour_scheme;
+
+            % Operators, u side
+            e_u       = u.getBoundaryOperatorForScalarField('e', boundary);
+            tau_u     = u.getBoundaryOperator('tau', boundary);
+            h11_u     = u.getBorrowing(boundary);
+            nu_u      = u.getNormal(boundary);
+
+            E_u = u.E;
+            C_u = u.C;
+            m_tot_u = u.grid.N();
+
+            % Operators, v side
+            e_v       = v.getBoundaryOperatorForScalarField('e', neighbour_boundary);
+            tau_v     = v.getBoundaryOperator('tau', neighbour_boundary);
+            h11_v     = v.getBorrowing(neighbour_boundary);
+            nu_v      = v.getNormal(neighbour_boundary);
+
+            E_v = v.E;
+            C_v = v.C;
+            m_tot_v = v.grid.N();
+
+            % Fix {'e', 's'}, {'w', 'n'}, and {'x','x'} couplings
+            flipFlag = false;
+            e_v_flip = e_v;
+            if (strcmp(boundary,'s') && strcmp(neighbour_boundary,'e')) || ...
+               (strcmp(boundary,'e') && strcmp(neighbour_boundary,'s')) || ...
+               (strcmp(boundary,'w') && strcmp(neighbour_boundary,'n')) || ...
+               (strcmp(boundary,'n') && strcmp(neighbour_boundary,'w')) || ...
+               (strcmp(boundary,'s') && strcmp(neighbour_boundary,'s')) || ...
+               (strcmp(boundary,'n') && strcmp(neighbour_boundary,'n')) || ...
+               (strcmp(boundary,'w') && strcmp(neighbour_boundary,'w')) || ...
+               (strcmp(boundary,'e') && strcmp(neighbour_boundary,'e'))
+
+                flipFlag = true;
+                e_v_flip = fliplr(e_v);
+
+                t1 = tau_v(:,1:2:end-1);
+                t2 = tau_v(:,2:2:end);
+
+                t1 = fliplr(t1);
+                t2 = fliplr(t2);
+
+                tau_v(:,1:2:end-1) = t1;
+                tau_v(:,2:2:end) = t2;
+            end
+
+            % Operators that are only required for own domain
+            Hi      = u.Hi_kron;
+            RHOi    = u.RHOi_kron;
+            e_kron  = u.getBoundaryOperator('e', boundary);
+            T_u     = u.getBoundaryTractionOperator(boundary);
+
+            % Shared operators
+            H_gamma         = u.getBoundaryQuadratureForScalarField(boundary);
+            H_gamma_kron    = u.getBoundaryQuadrature(boundary);
+            dim             = u.dim;
+
+            % Preallocate
+            [~, m_int] = size(H_gamma);
+            closure = sparse(dim*m_tot_u, dim*m_tot_u);
+            penalty = sparse(dim*m_tot_u, dim*m_tot_v);
+
+            % ---- Continuity of displacement ------
+
+            % Y: symmetrizing part of penalty
+            % Z: symmetric part of penalty
+            % X = Y + Z.
+
+            % Loop over components to couple across interface
+            for j = 1:dim
+
+                % Loop over components that penalties end up on
+                for i = 1:dim
+                    Y = 1/2*T_u{j,i}';
+                    Z_u = sparse(m_int, m_int);
+                    Z_v = sparse(m_int, m_int);
+                    for l = 1:dim
+                        for k = 1:dim
+                            Z_u = Z_u + e_u'*nu_u(l)*C_u{l,i,k,j}*nu_u(k)*e_u;
+                            Z_v = Z_v + e_v'*nu_v(l)*C_v{l,i,k,j}*nu_v(k)*e_v;
+                        end
+                    end
+
+                    if flipFlag
+                        Z_v = rot90(Z_v,2);
+                    end
+
+                    Z = -tuning*dim*( 1/(4*h11_u)*Z_u + 1/(4*h11_v)*Z_v );
+                    X = Y + Z*e_u';
+                    closure = closure + E_u{i}*X'*H_gamma*e_u'*E_u{j}';
+                    penalty = penalty - E_u{i}*X'*H_gamma*e_v_flip'*E_v{j}';
+
+                end
+            end
+
+            % ---- Continuity of traction ------
+            closure = closure - 1/2*e_kron*H_gamma_kron*tau_u';
+            penalty = penalty - 1/2*e_kron*H_gamma_kron*tau_v';
+
+            % ---- Multiply by inverse of density x quadraure ----
+            closure = RHOi*Hi*closure;
+            penalty = RHOi*Hi*penalty;
+
+        end
+
+        function [closure, penalty] = interfaceNonConforming(obj,boundary,neighbour_scheme,neighbour_boundary,type)
+            error('Non-conforming interfaces not implemented yet.');
+        end
+
+        % Returns the component number that is the tangential/normal component
+        % at the specified boundary
+        function comp = getComponent(obj, comp_str, boundary)
+            assertIsMember(comp_str, {'normal', 'tangential'});
+            assertIsMember(boundary, {'w', 'e', 's', 'n'});
+
+            switch boundary
+            case {'w', 'e'}
+                switch comp_str
+                case 'normal'
+                    comp = 1;
+                case 'tangential'
+                    comp = 2;
+                end
+            case {'s', 'n'}
+                switch comp_str
+                case 'normal'
+                    comp = 2;
+                case 'tangential'
+                    comp = 1;
+                end
+            end
+        end
+
+        % Returns h11 for the boundary specified by the string boundary.
+        % op -- string
+        function h11 = getBorrowing(obj, boundary)
+            assertIsMember(boundary, {'w', 'e', 's', 'n'})
+
+            switch boundary
+            case {'w','e'}
+                h11 = obj.h11{1};
+            case {'s', 'n'}
+                h11 = obj.h11{2};
+            end
+        end
+
+        % Returns the outward unit normal vector for the boundary specified by the string boundary.
+        function nu = getNormal(obj, boundary)
+            assertIsMember(boundary, {'w', 'e', 's', 'n'})
+
+            switch boundary
+            case 'w'
+                nu = [-1,0];
+            case 'e'
+                nu = [1,0];
+            case 's'
+                nu = [0,-1];
+            case 'n'
+                nu = [0,1];
+            end
+        end
+
+        % Returns the boundary operator op for the boundary specified by the string boundary.
+        % op -- string
+        function o = getBoundaryOperator(obj, op, boundary)
+            assertIsMember(boundary, {'w', 'e', 's', 'n'})
+            assertIsMember(op, {'e', 'e1', 'e2', 'tau', 'tau1', 'tau2'})
+
+            switch op
+                case {'e', 'e1', 'e2', 'tau', 'tau1', 'tau2'}
+                    o = obj.([op, '_', boundary]);
+            end
+
+        end
+
+        % Returns the boundary operator op for the boundary specified by the string boundary.
+        % op -- string
+        function o = getBoundaryOperatorForScalarField(obj, op, boundary)
+            assertIsMember(boundary, {'w', 'e', 's', 'n'})
+            assertIsMember(op, {'e_u', 'e_s'})
+
+            switch op
+                case 'e_u'
+                    o = obj.(['e_', boundary, '_u']);
+                case 'e_s'
+                    o = obj.(['e_', boundary, '_s']);
+            end
+
+        end
+
+        % Returns the boundary operator T_ij (cell format) for the boundary specified by the string boundary.
+        % Formula: tau_i = T_ij u_j
+        % op -- string
+        function T = getBoundaryTractionOperator(obj, boundary)
+            assertIsMember(boundary, {'w', 'e', 's', 'n'})
+
+            T = obj.(['T', '_', boundary]);
+        end
+
+        % Returns square boundary quadrature matrix, of dimension
+        % corresponding to the number of boundary unknowns
+        %
+        % boundary -- string
+        function H = getBoundaryQuadrature(obj, boundary)
+            assertIsMember(boundary, {'w', 'e', 's', 'n'})
+
+            H = obj.getBoundaryQuadratureForScalarField(boundary);
+            I_dim = speye(obj.dim, obj.dim);
+            H = kron(H, I_dim);
+        end
+
+        % Returns square boundary quadrature matrix, of dimension
+        % corresponding to the number of boundary grid points
+        %
+        % boundary -- string
+        function H_b = getBoundaryQuadratureForScalarField(obj, boundary)
+            assertIsMember(boundary, {'w', 'e', 's', 'n'})
+
+            H_b = obj.(['H_', boundary, '_s']);
+        end
+
+        function N = size(obj)
+            N = obj.dim*prod(obj.m);
+        end
+    end
+end