sbplib: +scheme/Beam.m comparison

comparison +scheme/Beam.m @ 832:5573913a0949 feature/burgers1d

Merged with default, and updated +scheme/Burgers1D accordingly

author	Vidar Stiernström <vidar.stiernstrom@it.uu.se>
date	Tue, 11 Sep 2018 15:58:35 +0200
parents	4ced7d47bd1f
children	459eeb99130f

comparison

equal deleted inserted replaced

-:d0934d1143b7
+:5573913a0949
+classdef Beam < scheme.Scheme
+properties
+order % Order accuracy for the approximation
+grid
+D % non-stabalized scheme operator
+alpha
+h
+H % Discrete norm
+Hi
+e_l,  e_r
+d1_l, d1_r
+d2_l, d2_r
+d3_l, d3_r
+gamm
+delt
+alphaII
+alphaIII
+opt
+end
+methods
+function obj = Beam(grid, order, alpha, opsGen, opt)
+default_arg('alpha', -1);
+% default_arg('opsGen', @sbp.D4);
+default_arg('opsGen', @sbp.D4Variable); % Supposed to be better
+opt_default.interface_l.tuning = 1.1;
+opt_default.interface_l.tau = [];
+opt_default.interface_l.sig = [];
+opt_default.interface_r.tuning = 1.1;
+opt_default.interface_r.tau = [];
+opt_default.interface_r.sig = [];
+default_struct('opt', opt_default);
+if ~isa(grid, 'grid.Cartesian') || grid.D() ~= 1
+error('Grid must be 1d cartesian');
+end
+obj.grid = grid;
+obj.order = order;
+obj.alpha = alpha;
+m = grid.m;
+h = grid.scaling();
+x_lim = {grid.x{1}(1), grid.x{1}(end)};
+ops = opsGen(m, x_lim, order);
+D4       = ops.D4;
+obj.H    = ops.H;
+obj.Hi   = ops.HI;
+obj.e_l  = ops.e_l;
+obj.e_r  = ops.e_r;
+obj.d1_l = ops.d1_l;
+obj.d1_r = ops.d1_r;
+obj.d2_l = ops.d2_l;
+obj.d2_r = ops.d2_r;
+obj.d3_l = ops.d3_l;
+obj.d3_r = ops.d3_r;
+obj.D = alpha*D4;
+alphaII  = ops.borrowing.N.S2/2;
+alphaIII = ops.borrowing.N.S3/2;
+obj.gamm = h*alphaII;
+obj.delt = h^3*alphaIII;
+obj.alphaII = alphaII;
+obj.alphaIII = alphaIII;
+obj.h = h;
+obj.opt = opt;
+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.
+%       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)
+default_arg('type','dn');
+[e, d1, d2, d3, s] = obj.get_boundary_ops(boundary);
+gamm = obj.gamm;
+delt = obj.delt;
+% TODO: Can this be simplifed? Can I handle conditions on u on its own, u_x on its own ...
+switch type
+case {'dn', 'clamped'} % Dirichlet-neumann boundary condition
+alpha = obj.alpha;
+% tau1 < -alpha^2/gamma
+% tuning = 2;
+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 = obj.Hi*(tau*e' + sig*d1');
+penalty{1} = -obj.Hi*tau;
+penalty{2} = -obj.Hi*sig;
+case {'free'}
+a = obj.alpha;
+tau =  s*a*d1;
+sig = -s*a*e;
+closure = obj.Hi*(tau*d2' + sig*d3');
+penalty{1} = -obj.Hi*tau;
+penalty{1} = -obj.Hi*sig;
+case 'e'
+alpha = obj.alpha;
+tuning = 1.1;
+tau1 = tuning * alpha/delt;
+tau4 = s*alpha;
+tau = tau1*e+tau4*d3;
+closure = obj.Hi*tau*e';
+penalty = -obj.Hi*tau;
+case 'd1'
+alpha = obj.alpha;
+tuning = 1.1;
+sig2 = tuning * alpha/gamm;
+sig3 = -s*alpha;
+sig = sig2*d1+sig3*d2;
+closure = obj.Hi*sig*d1';
+penalty = -obj.Hi*sig;
+case 'd2'
+a = obj.alpha;
+tau =  s*a*d1;
+closure = obj.Hi*tau*d2';
+penalty = -obj.Hi*tau;
+case 'd3'
+a = obj.alpha;
+sig = -s*a*e;
+closure = obj.Hi*sig*d3';
+penalty = -obj.Hi*sig;
+otherwise % Unknown, boundary condition
+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] = obj.get_boundary_ops(boundary);
+[e_v,d1_v,d2_v,d3_v,s_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
+alpha_u = obj.alpha;
+alpha_v = neighbour_scheme.alpha;
+switch boundary
+case 'l'
+interface_opt = obj.opt.interface_l;
+case 'r'
+interface_opt = obj.opt.interface_r;
+end
+if isempty(interface_opt.tau) && isempty(interface_opt.sig)
+gamm_u = obj.gamm;
+delt_u = obj.delt;
+gamm_v = neighbour_scheme.gamm;
+delt_v = neighbour_scheme.delt;
+tuning = interface_opt.tuning;
+tau1 = ((alpha_u/2)/delt_u + (alpha_v/2)/delt_v)/2*tuning;
+sig2 = ((alpha_u/2)/gamm_u + (alpha_v/2)/gamm_v)/2*tuning;
+else
+h_u = obj.h;
+h_v = neighbour_scheme.h;
+switch neighbour_boundary
+case 'l'
+neighbour_interface_opt = neighbour_scheme.opt.interface_l;
+case 'r'
+neighbour_interface_opt = neighbour_scheme.opt.interface_r;
+end
+tau_u = interface_opt.tau;
+sig_u = interface_opt.sig;
+tau_v = neighbour_interface_opt.tau;
+sig_v = neighbour_interface_opt.sig;
+tau1 = tau_u/h_u^3 + tau_v/h_v^3;
+sig2 = sig_u/h_u   + sig_v/h_v;
+end
+tau4 = s_u*alpha_u/2;
+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 =  obj.Hi*(tau*e_u' + sig*d1_u' + phi*alpha_u*d2_u' + psi*alpha_u*d3_u');
+penalty = -obj.Hi*(tau*e_v' + sig*d1_v' + phi*alpha_v*d2_v' + psi*alpha_v*d3_v');
+end
+% Returns 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] = get_boundary_ops(obj,boundary)
+switch boundary
+case 'l'
+e  = obj.e_l;
+d1 = obj.d1_l;
+d2 = obj.d2_l;
+d3 = obj.d3_l;
+s = -1;
+case 'r'
+e  = obj.e_r;
+d1 = obj.d1_r;
+d2 = obj.d2_r;
+d3 = obj.d3_r;
+s = 1;
+otherwise
+error('No such boundary: boundary = %s',boundary);
+end
+end
+function N = size(obj)
+N = obj.grid.N;
+end
+end
+end

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comparison +scheme/Beam.m @ 832:5573913a0949 feature/burgers1d