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comparison +scheme/Schrodinger1dCurve.m @ 429:dde5760863de feature/quantumTriangles

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Added a scheme for the time deforming shrodinger equation in 1d
author Ylva Rydin <ylva.rydin@telia.com>
date Mon, 06 Feb 2017 09:54:18 +0100
parents
children 25053554524b
comparison
equal deleted inserted replaced
428:a39fe3bcbd95 429:dde5760863de
1 classdef Schrodinger1dCurve < scheme.Scheme
2 properties
3 m % Number of points in each direction, possibly a vector
4 h % Grid spacing
5 xi % Grid
6 order % Order accuracy for the approximation
7 grid
8
9 D % non-stabalized scheme operator
10 H % Discrete norm
11 M % Derivative norm
12 alpha
13
14 V_mat
15 D1
16 D2
17 Hi
18 e_l
19 e_r
20 d1_l
21 d1_r
22 gamm
23 end
24
25 methods
26 % Solving SE in the form u_t = i*u_xx +i*V on deforming 1D domain;
27 function obj = Schrodinger1dCurve(m,order,V,constJi)
28 default_arg('V',0);
29 default_arg('constJi',false)
30 xilim={0 1};
31 if constJi
32 ops = sbp.D2Standard(m,xilim,order);
33 else
34 ops = sbp.D4Variable(m,xilim,order);
35 end
36
37 obj.xi=ops.x;
38 obj.h=ops.h;
39 obj.D2 = ops.D2;
40 obj.D1 = ops.D1;
41 obj.H = ops.H;
42 obj.Hi = ops.HI;
43 obj.M = ops.M;
44 obj.e_l = ops.e_l;
45 obj.e_r = ops.e_r;
46 obj.d1_l = ops.d1_l;
47 obj.d1_r = ops.d1_r;
48
49
50 if isa(V,'function_handle')
51 V_vec = V(obj.x);
52 else
53 V_vec = obj.xi*0 + V;
54 end
55
56 obj.V_mat = spdiags(V_vec,0,m,m);
57
58 obj.D = @(a,a_xi,Ji) obj.d_fun(a, a_xi, Ji, constJi);
59
60 obj.m = m;
61 obj.order = order;
62 end
63
64
65 % Closure functions return the opertors appliedo to the own doamin to close the boundary
66 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
67 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
68 % type is a string specifying the type of boundary condition if there are several.
69 % data is a function returning the data that should be applied at the boundary.
70 % neighbour_scheme is an instance of Scheme that should be interfaced to.
71 % neighbour_boundary is a string specifying which boundary to interface to.
72
73 function [D] = d_fun(obj,a, a_xi , Ji , constJi)
74 if constJi
75 D= -0.5*(obj.D1*a - a_xi + a*obj.D1) + 1i*Ji*obj.D2 + 1i*obj.V_mat;
76 % D= -a*obj.D1 + 1i*Ji*obj.D2 + 1i*obj.V_mat;
77 else
78 D= -0.5*(obj.D1*a - a_xi + a*obj.D1) + 1i*obj.D2(diag(Ji)) + 1i*obj.V_mat;
79 % D= - a*obj.D1 + 1i*obj.D2(diag(Ji)) + 1i*obj.V_mat;
80 % D=-obj.D1*a - a_xi + 1i*obj.D2(diag(Ji)) + 1i*obj.V_mat;
81 end
82 end
83
84 function [closure, penalty] = boundary_condition(obj,boundary,type,data)
85 default_arg('type','dirichlet');
86 default_arg('data',0);
87
88 [e,d,s,p] = obj.get_boundary_ops(boundary);
89
90 switch type
91 % Dirichlet boundary condition
92 case {'D','d','dirichlet'}
93 tau1 = s * 1i*d;
94 tau2 = @(a) (-1*s*a(p,p) - abs(a(p,p)))/4*e;
95 closure = @(a) obj.Hi*tau1*e' + obj.Hi*tau2(a)*e';
96
97 switch class(data)
98 case 'double'
99 penalty = @(a) -(obj.Hi*tau1*data+obj.Hi*tau2(a)*data);
100 % case 'function_handle'
101 % penalty = @(t)-obj.Hi*tau*data(t);
102 otherwise
103 error('Wierd data argument!')
104 end
105
106 % Unknown, boundary condition
107 otherwise
108 error('No such boundary condition: type = %s',type);
109 end
110 end
111
112 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
113 % u denotes the solution in the own domain
114 % v denotes the solution in the neighbour domain
115 % [e_u,d_u,s_u] = obj.get_boundary_ops(boundary);
116 % [e_v,d_v,s_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
117
118 % a = -s_u* 1/2 * 1i ;
119 % b = a';
120
121 % tau = b*d_u;
122 % sig = -a*e_u;
123
124 % closure = obj.Hi * (tau*e_u' + sig*d_u');
125 % penalty = obj.Hi * (-tau*e_v' - sig*d_v');
126 end
127
128 % Ruturns the boundary ops and sign for the boundary specified by the string boundary.
129 % The right boundary is considered the positive boundary
130 function [e,d,s,p] = get_boundary_ops(obj,boundary)
131 switch boundary
132 case 'l'
133 e = obj.e_l;
134 d = obj.d1_l;
135 s = -1;
136 p=1;
137 case 'r'
138 e = obj.e_r;
139 d = obj.d1_r;
140 s = 1;
141 p=obj.m;
142 otherwise
143 error('No such boundary: boundary = %s',boundary);
144 end
145 end
146
147 function N = size(obj)
148 N = obj.m;
149 end
150
151 end
152
153 methods(Static)
154 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u
155 % and bound_v of scheme schm_v.
156 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l')
157 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
158 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
159 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
160 end
161 end
162 end