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comparison +scheme/Schrodinger.m @ 0:48b6fb693025

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Initial commit.
author Jonatan Werpers <jonatan@werpers.com>
date Thu, 17 Sep 2015 10:12:50 +0200
parents
children 33f0654a2413
comparison
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-1:000000000000 0:48b6fb693025
1 classdef Schrodinger < noname.Scheme
2 properties
3 m % Number of points in each direction, possibly a vector
4 h % Grid spacing
5 x % Grid
6 order % Order accuracy for the approximation
7
8 D % non-stabalized scheme operator
9 H % Discrete norm
10 M % Derivative norm
11 alpha
12
13 Hi
14 e_l
15 e_r
16 d1_l
17 d1_r
18 gamm
19 end
20
21 methods
22 % Solving SE in the form u_t = i*u_xx -i*V;
23 function obj = Schrodinger(m,xlim,order,V)
24 default_arg('V',0);
25
26 [x, h] = util.get_grid(xlim{:},m);
27
28 ops = sbp.Ordinary(m,h,order);
29
30 obj.D2 = sparse(ops.derivatives.D2);
31 obj.H = sparse(ops.norms.H);
32 obj.Hi = sparse(ops.norms.HI);
33 obj.M = sparse(ops.norms.M);
34 obj.e_l = sparse(ops.boundary.e_1);
35 obj.e_r = sparse(ops.boundary.e_m);
36 obj.d1_l = sparse(ops.boundary.S_1);
37 obj.d1_r = sparse(ops.boundary.S_m);
38
39
40 if isa(V,'function_handle')
41 V_vec = V(x);
42 else
43 V_vec = x*0 + V;
44 end
45
46 V_mat = spdiags(V,0,m,m);
47
48
49 D = 1i * obj.D2 - 1i * V;
50
51 obj.m = m;
52 obj.h = h;
53 obj.order = order;
54
55 obj.D = alpha*obj.D2;
56 obj.x = x;
57 end
58
59
60 % Closure functions return the opertors applied to the own doamin to close the boundary
61 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
62 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
63 % type is a string specifying the type of boundary condition if there are several.
64 % data is a function returning the data that should be applied at the boundary.
65 % neighbour_scheme is an instance of Scheme that should be interfaced to.
66 % neighbour_boundary is a string specifying which boundary to interface to.
67 function [closure, penalty] = boundary_condition(obj,boundary,type,data)
68 default_arg('type','neumann');
69 default_arg('data',0);
70
71 [e,d,s] = obj.get_boundary_ops(boundary);
72
73 switch type
74 % Dirichlet boundary condition
75 case {'D','d','dirichlet'}
76 tau = -1i* s * d;
77
78 closure = obj.Hi*tau*e';
79
80 pp = obj.Hi*p;
81 switch class(data)
82 case 'double'
83 penalty = pp*data;
84 case 'function_handle'
85 penalty = @(t)pp*data(t);
86 otherwise
87 error('Wierd data argument!')
88 end
89
90 % Unknown, boundary condition
91 otherwise
92 error('No such boundary condition: type = %s',type);
93 end
94 end
95
96 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
97 % u denotes the solution in the own domain
98 % v denotes the solution in the neighbour domain
99 [e_u,d_u,s_u] = obj.get_boundary_ops(boundary);
100 [e_v,d_v,s_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
101
102 a = s/2 * 1i ;
103 b = - a';
104
105 tau = b*d_u;
106 sig = a*e_u;
107
108 closure = obj.Hi * (tau*e_u' + sig*d_u');
109 penalty = obj.Hi * (-tau*e_v' - sig*d_v');
110 end
111
112 % Ruturns the boundary ops and sign for the boundary specified by the string boundary.
113 % The right boundary is considered the positive boundary
114 function [e,d,s] = get_boundary_ops(obj,boundary)
115 switch boundary
116 case 'l'
117 e = obj.e_l;
118 d = obj.d1_l;
119 s = -1;
120 case 'r'
121 e = obj.e_r;
122 d = obj.d1_r;
123 s = 1;
124 otherwise
125 error('No such boundary: boundary = %s',boundary);
126 end
127 end
128
129 function N = size(obj)
130 N = obj.m;
131 end
132
133 end
134
135 methods(Static)
136 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u
137 % and bound_v of scheme schm_v.
138 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l')
139 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
140 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
141 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
142 end
143 end
144 end