sbplib: +scheme/Utux2D.m annotate

author	Martin Almquist <martin.almquist@it.uu.se>
date	Mon, 11 Sep 2017 14:12:54 +0200
parents
children	2a2f34778ded

rev	line source
591 39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	1 classdef Utux2D < scheme.Scheme
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	2 properties
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	3 m % Number of points in each direction, possibly a vector
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	4 h % Grid spacing
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	5 grid % Grid
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	6 order % Order accuracy for the approximation
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	7 v0 % Initial data
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	8
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	9 a % Wave speed a = [a1, a2];
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	10
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	11 H % Discrete norm
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	12 Hi, Hx, Hy, Hxi, Hyi
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	13
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	14 % Derivatives
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	15 Dx, Dy
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	16
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	17 % Boundary operators
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	18 e_w, e_e, e_s, e_n
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	19
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	20 D % Total discrete operator
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	21
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	22 end
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	23
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	24
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	25 methods
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	26 function obj = Utux2D(g ,order, opSet, a)
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	27
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	28 default_arg('a',1/sqrt(2)*[1, 1]);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	29 default_arg('opSet',@sbp.D2Standard);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	30 assert(isa(g, 'grid.Cartesian'))
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	31
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	32 m = g.size();
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	33 m_x = m(1);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	34 m_y = m(2);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	35 m_tot = g.N();
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	36
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	37 xlim = g.x{1};
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	38 ylim = g.x{2};
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	39 obj.grid = g;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	40
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	41 % Operator sets
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	42 ops_x = opSet(m_x, xlim, order);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	43 ops_y = opSet(m_y, ylim, order);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	44 Ix = speye(m_x);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	45 Iy = speye(m_y);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	46
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	47 % Norms
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	48 Hx = ops_x.H;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	49 Hy = ops_y.H;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	50 Hxi = ops_x.HI;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	51 Hyi = ops_y.HI;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	52 obj.H = kron(Hx,Hy);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	53 obj.Hi = kron(Hxi,Hyi);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	54 obj.Hx = kron(Hx,Iy);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	55 obj.Hy = kron(Ix,Hy);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	56 obj.Hxi = kron(Hxi,Iy);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	57 obj.Hyi = kron(Ix,Hyi);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	58
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	59 % Derivatives
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	60 Dx = ops_x.D1;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	61 Dy = ops_y.D1;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	62 obj.Dx = kron(Dx,Iy);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	63 obj.Dy = kron(Ix,Dy);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	64
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	65 % Boundary operators
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	66 obj.e_w = kr(ops_x.e_l, Iy);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	67 obj.e_e = kr(ops_x.e_r, Iy);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	68 obj.e_s = kr(Ix, ops_y.e_l);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	69 obj.e_n = kr(Ix, ops_y.e_r);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	70
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	71 obj.m = m;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	72 obj.h = [ops_x.h ops_y.h];
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	73 obj.order = order;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	74
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	75 obj.D = -(a(1)obj.Dx + a(2)obj.Dy);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	76
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	77 end
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	78 % Closure functions return the opertors applied to the own domain to close the boundary
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	79 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	80 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	81 % type is a string specifying the type of boundary condition if there are several.
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	82 % data is a function returning the data that should be applied at the boundary.
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	83 % neighbour_scheme is an instance of Scheme that should be interfaced to.
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	84 % neighbour_boundary is a string specifying which boundary to interface to.
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	85 function [closure, penalty] = boundary_condition(obj,boundary,type)
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	86 default_arg('type','dirichlet');
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	87
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	88 sigma = -1; % Scalar penalty parameter
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	89 switch boundary
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	90 case {'w','W','west','West'}
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	91 tau = sigmaobj.a(1)obj.e_w*obj.Hy;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	92 closure = obj.Hitauobj.e_w';
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	93
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	94 case {'s','S','south','South'}
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	95 tau = sigmapbj.a(2)obj.e_s*obj.Hx;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	96 closure = obj.Hitauobj.e_s';
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	97 end
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	98 penalty = -obj.Hi*tau;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	99
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	100 end
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	101
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	102 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	103
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	104 % Get neighbour boundary operator
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	105 switch neighbour_boundary
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	106 case {'e','E','east','East'}
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	107 e_neighbour = neighbour_scheme.e_e;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	108 case {'w','W','west','West'}
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	109 e_neighbour = neighbour_scheme.e_w;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	110 case {'n','N','north','North'}
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	111 e_neighbour = neighbour_scheme.e_n;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	112 case {'s','S','south','South'}
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	113 e_neighbour = neighbour_scheme.e_s;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	114 end
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	115
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	116 % Upwind coupling
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	117 sigma_ds = -1; %"Downstream" penalty
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	118 sigma_us = 0; %"Upstream" penalty
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	119
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	120 switch boundary
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	121 case {'w','W','west','West'}
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	122 tau = sigma_dsobj.a(1)obj.e_w*obj.Hy;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	123 closure = obj.Hitauobj.e_w';
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	124 case {'e','E','east','East'}
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	125 tau = sigma_usobj.a(1)obj.e_e*obj.Hy;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	126 closure = obj.Hitauobj.e_e';
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	127 case {'s','S','south','South'}
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	128 tau = sigma_dsobj.a(2)obj.e_s*obj.Hx;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	129 closure = obj.Hitauobj.e_s';
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	130 case {'n','N','north','North'}
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	131 tau = sigma_usobj.a(2)obj.e_n*obj.Hx;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	132 closure = obj.Hitauobj.e_n';
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	133 end
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	134 penalty = -obj.Hitaue_neighbour';
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	135
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	136 end
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	137
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	138 function N = size(obj)
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	139 N = obj.m;
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	140 end
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	141
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	142 end
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	143
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	144 methods(Static)
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	145 % Calculates the matrices needed for the inteface coupling between boundary bound_u of scheme schm_u
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	146 % and bound_v of scheme schm_v.
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	147 % [uu, uv, vv, vu] = inteface_coupling(A,'r',B,'l')
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	148 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	149 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	150 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	151 end
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	152 end
39554f2de783 Add Utux2D scheme Martin Almquist <martin.almquist@it.uu.se> parents: diff changeset	153 end

591

39554f2de783 Add Utux2D scheme