Mercurial > repos > public > sbplib
changeset 450:8d455e49364f feature/grids
Copy Wave2dCurve to new scheme LaplaceCurvilinear
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Tue, 09 May 2017 14:58:27 +0200 |
| parents | 0707a7192bc3 |
| children | 4e266dfe9edc |
| files | +scheme/LaplaceCurvilinear.m +scheme/Wave2dCurve.m |
| diffstat | 2 files changed, 358 insertions(+), 0 deletions(-) [+] |
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diff -r 0707a7192bc3 -r 8d455e49364f +scheme/LaplaceCurvilinear.m --- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/+scheme/LaplaceCurvilinear.m Tue May 09 14:58:27 2017 +0200 @@ -0,0 +1,356 @@ +classdef LaplaceCurvilinear < 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 + c + J, Ji + a11, a12, a22 + + 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 + e_w, e_e, e_s, e_n + du_w, dv_w + du_e, dv_e + du_s, dv_s + du_n, dv_n + gamm_u, gamm_v + lambda + + Dx, Dy % Physical derivatives + + x_u + x_v + y_u + y_v + end + + methods + function obj = LaplaceCurvilinear(g ,order, c, opSet) + default_arg('opSet',@sbp.D2Variable); + default_arg('c', 1); + + assert(isa(g, 'grid.Curvilinear')) + + 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; + D2_u = ops_u.D2; + 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; + + D1_v = ops_v.D1; + 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; + + Du = kr(D1_u,I_v); + Dv = kr(I_u,D1_v); + + % Metric derivatives + coords = g.points(); + x = coords(:,1); + y = coords(:,2); + + x_u = Du*x; + x_v = Dv*x; + y_u = Du*y; + y_v = 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 = Du*L_12*Dv; + Dvu = Dv*L_12*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 + + 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; + + obj.c = c; + obj.J = spdiags(J, 0, m_tot, m_tot); + obj.Ji = spdiags(1./J, 0, m_tot, m_tot); + obj.a11 = a11; + obj.a12 = a12; + obj.a22 = a22; + obj.D = obj.Ji*c^2*(Duu + Duv + Dvu + Dvv); + obj.lambda = lambda; + + obj.Dx = spdiag( y_v./J)*Du + spdiag(-y_u./J)*Dv; + obj.Dy = spdiag(-x_v./J)*Du + spdiag( x_u./J)*Dv; + + 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, type, parameter) + default_arg('type','neumann'); + default_arg('parameter', []); + + [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv , ~, ~, ~, scale_factor] = obj.get_boundary_ops(boundary); + switch type + % Dirichlet boundary condition + case {'D','d','dirichlet'} + % 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] = 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; + + tau = -1./b1 - 1./b2; + tau = tuning * spdiag(tau); + sig1 = 1; + + penalty_parameter_1 = halfnorm_inv_n*(tau + sig1*halfnorm_inv_t*F*e'*halfnorm_t)*e; + + closure = obj.Ji*obj.c^2 * penalty_parameter_1*e'; + penalty = -obj.Ji*obj.c^2 * penalty_parameter_1; + + + % Neumann boundary condition + case {'N','n','neumann'} + c = obj.c; + + a_n = spdiags(coeff_n,0,length(coeff_n),length(coeff_n)); + a_t = spdiags(coeff_t,0,length(coeff_t),length(coeff_t)); + d = (a_n * d_n' + a_t*d_t')'; + + tau1 = -s; + tau2 = 0; + tau = c.^2 * obj.Ji*(tau1*e + tau2*d); + + closure = halfnorm_inv*tau*d'; + penalty = -halfnorm_inv*tau; + + % Characteristic boundary condition + case {'characteristic', 'char', 'c'} + default_arg('parameter', 1); + beta = parameter; + c = obj.c; + + a_n = spdiags(coeff_n,0,length(coeff_n),length(coeff_n)); + a_t = spdiags(coeff_t,0,length(coeff_t),length(coeff_t)); + d = s*(a_n * d_n' + a_t*d_t')'; % outward facing normal derivative + + tau = -c.^2 * 1/beta*obj.Ji*e; + + closure{1} = halfnorm_inv*tau/c*spdiag(scale_factor)*e'; + closure{2} = halfnorm_inv*tau*beta*d'; + penalty = -halfnorm_inv*tau; + + % 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 + tuning = 1.2; + % tuning = 20.2; + [e_u, d_n_u, d_t_u, coeff_n_u, coeff_t_u, s_u, gamm_u, halfnorm_inv_u_n, halfnorm_inv_u_t, halfnorm_u_t, I_u] = obj.get_boundary_ops(boundary); + [e_v, d_n_v, d_t_v, coeff_n_v, coeff_t_v, s_v, gamm_v, halfnorm_inv_v_n, halfnorm_inv_v_t, halfnorm_v_t, I_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary); + + a_n_u = spdiag(coeff_n_u); + a_t_u = spdiag(coeff_t_u); + a_n_v = spdiag(coeff_n_v); + a_t_v = spdiag(coeff_t_v); + + F_u = (s_u * a_n_u * d_n_u' + s_u * a_t_u*d_t_u')'; + F_v = (s_v * a_n_v * d_n_v' + s_v * a_t_v*d_t_v')'; + + u = obj; + v = neighbour_scheme; + + b1_u = gamm_u*u.lambda(I_u)./u.a11(I_u).^2; + b2_u = gamm_u*u.lambda(I_u)./u.a22(I_u).^2; + b1_v = gamm_v*v.lambda(I_v)./v.a11(I_v).^2; + b2_v = gamm_v*v.lambda(I_v)./v.a22(I_v).^2; + + tau = -1./(4*b1_u) -1./(4*b1_v) -1./(4*b2_u) -1./(4*b2_v); + tau = tuning * spdiag(tau); + sig1 = 1/2; + sig2 = -1/2; + + penalty_parameter_1 = halfnorm_inv_u_n*(e_u*tau + sig1*halfnorm_inv_u_t*F_u*e_u'*halfnorm_u_t*e_u); + penalty_parameter_2 = halfnorm_inv_u_n * sig2 * e_u; + + + closure = obj.Ji*obj.c^2 * ( penalty_parameter_1*e_u' + penalty_parameter_2*F_u'); + penalty = obj.Ji*obj.c^2 * (-penalty_parameter_1*e_v' + penalty_parameter_2*F_v'); + end + + % Ruturns the boundary ops and sign for the boundary specified by the string boundary. + % The right boundary is considered the positive boundary + % + % I -- the indecies of the boundary points in the grid matrix + function [e, d_n, d_t, coeff_n, coeff_t, s, gamm, halfnorm_inv_n, halfnorm_inv_t, halfnorm_t, I, scale_factor] = 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; + case {'s','n'} + halfnorm_inv_n = obj.Hiv; + halfnorm_inv_t = obj.Hiu; + halfnorm_t = obj.Hu; + gamm = obj.gamm_v; + end + end + + function N = size(obj) + N = prod(obj.m); + end + + + end +end \ No newline at end of file
diff -r 0707a7192bc3 -r 8d455e49364f +scheme/Wave2dCurve.m --- a/+scheme/Wave2dCurve.m Tue May 09 14:51:29 2017 +0200 +++ b/+scheme/Wave2dCurve.m Tue May 09 14:58:27 2017 +0200 @@ -40,6 +40,8 @@ default_arg('opSet',@sbp.D2Variable); default_arg('c', 1); + warning('Use LaplaceCruveilinear instead') + assert(isa(g, 'grid.Curvilinear')) m = g.size();