Mercurial > repos > public > sbplib
annotate +scheme/Schrodinger.m @ 999:337c4d1dcef5 feature/getBoundaryOp
Fix overlooked Schrodinger1d scheme.
| author | Martin Almquist <malmquist@stanford.edu> |
|---|---|
| date | Sat, 12 Jan 2019 13:44:08 -0800 |
| parents | 706d1c2b4199 |
| children | 8d73fcdb07a5 |
| rev | line source |
|---|---|
|
65
33f0654a2413
Fixed mistakes in Schrodinger scheme. BC are now working.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
1 classdef Schrodinger < scheme.Scheme |
| 0 | 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 | |
|
65
33f0654a2413
Fixed mistakes in Schrodinger scheme. BC are now working.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
13 D2 |
| 0 | 14 Hi |
| 15 e_l | |
| 16 e_r | |
| 17 d1_l | |
| 18 d1_r | |
| 19 gamm | |
| 20 end | |
| 21 | |
| 22 methods | |
| 23 % Solving SE in the form u_t = i*u_xx -i*V; | |
| 24 function obj = Schrodinger(m,xlim,order,V) | |
| 25 default_arg('V',0); | |
| 26 | |
| 27 [x, h] = util.get_grid(xlim{:},m); | |
| 28 | |
| 29 ops = sbp.Ordinary(m,h,order); | |
| 30 | |
| 31 obj.D2 = sparse(ops.derivatives.D2); | |
| 32 obj.H = sparse(ops.norms.H); | |
| 33 obj.Hi = sparse(ops.norms.HI); | |
| 34 obj.M = sparse(ops.norms.M); | |
| 35 obj.e_l = sparse(ops.boundary.e_1); | |
| 36 obj.e_r = sparse(ops.boundary.e_m); | |
| 37 obj.d1_l = sparse(ops.boundary.S_1); | |
| 38 obj.d1_r = sparse(ops.boundary.S_m); | |
| 39 | |
| 40 | |
| 41 if isa(V,'function_handle') | |
| 42 V_vec = V(x); | |
| 43 else | |
| 44 V_vec = x*0 + V; | |
| 45 end | |
| 46 | |
|
65
33f0654a2413
Fixed mistakes in Schrodinger scheme. BC are now working.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
47 V_mat = spdiags(V_vec,0,m,m); |
| 0 | 48 |
|
67
446d67a49cd8
Fixed some errors in scheme.Schrodinger.m
Jonatan Werpers <jonatan@werpers.com>
parents:
65
diff
changeset
|
49 obj.D = 1i * obj.D2 - 1i * V_mat; |
| 0 | 50 |
| 51 obj.m = m; | |
| 52 obj.h = h; | |
| 53 obj.order = order; | |
| 54 | |
| 55 obj.x = x; | |
| 56 end | |
| 57 | |
| 58 | |
| 59 % Closure functions return the opertors applied to the own doamin to close the boundary | |
| 60 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. | |
| 61 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. | |
| 62 % type is a string specifying the type of boundary condition if there are several. | |
| 63 % data is a function returning the data that should be applied at the boundary. | |
| 64 % neighbour_scheme is an instance of Scheme that should be interfaced to. | |
| 65 % neighbour_boundary is a string specifying which boundary to interface to. | |
| 66 function [closure, penalty] = boundary_condition(obj,boundary,type,data) | |
|
65
33f0654a2413
Fixed mistakes in Schrodinger scheme. BC are now working.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
67 default_arg('type','dirichlet'); |
| 0 | 68 default_arg('data',0); |
| 69 | |
|
999
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
70 [e, d] = obj.getBoundaryOperator({'e', 'd'}, boundary); |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
71 s = obj.getBoundarySign(boundary); |
| 0 | 72 |
| 73 switch type | |
| 74 % Dirichlet boundary condition | |
| 75 case {'D','d','dirichlet'} | |
|
65
33f0654a2413
Fixed mistakes in Schrodinger scheme. BC are now working.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
76 tau = s * 1i*d; |
| 0 | 77 closure = obj.Hi*tau*e'; |
| 78 | |
| 79 switch class(data) | |
| 80 case 'double' | |
|
65
33f0654a2413
Fixed mistakes in Schrodinger scheme. BC are now working.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
81 penalty = -obj.Hi*tau*data; |
| 0 | 82 case 'function_handle' |
|
65
33f0654a2413
Fixed mistakes in Schrodinger scheme. BC are now working.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
83 penalty = @(t)-obj.Hi*tau*data(t); |
| 0 | 84 otherwise |
| 85 error('Wierd data argument!') | |
| 86 end | |
| 87 | |
| 88 % Unknown, boundary condition | |
| 89 otherwise | |
| 90 error('No such boundary condition: type = %s',type); | |
| 91 end | |
| 92 end | |
| 93 | |
|
946
706d1c2b4199
Raname opts to type in a bunch of interface methods
Jonatan Werpers <jonatan@werpers.com>
parents:
910
diff
changeset
|
94 function [closure, penalty] = interface(obj, boundary, neighbour_scheme, neighbour_boundary, type) |
| 0 | 95 % u denotes the solution in the own domain |
| 96 % v denotes the solution in the neighbour domain | |
|
999
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
97 [e_u, d_u] = obj.getBoundaryOperator({'e', 'd'}, boundary); |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
98 s_u = obj.getBoundarySign(boundary); |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
99 |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
100 [e_v, d_v] = neighbour_scheme.getBoundaryOperator({'e', 'd'}, neighbour_boundary); |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
101 s_v = neighbour_scheme.getBoundarySign(neighbour_boundary); |
| 0 | 102 |
|
67
446d67a49cd8
Fixed some errors in scheme.Schrodinger.m
Jonatan Werpers <jonatan@werpers.com>
parents:
65
diff
changeset
|
103 a = -s_u* 1/2 * 1i ; |
|
65
33f0654a2413
Fixed mistakes in Schrodinger scheme. BC are now working.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
104 b = a'; |
| 0 | 105 |
| 106 tau = b*d_u; | |
|
67
446d67a49cd8
Fixed some errors in scheme.Schrodinger.m
Jonatan Werpers <jonatan@werpers.com>
parents:
65
diff
changeset
|
107 sig = -a*e_u; |
| 0 | 108 |
| 109 closure = obj.Hi * (tau*e_u' + sig*d_u'); | |
| 110 penalty = obj.Hi * (-tau*e_v' - sig*d_v'); | |
| 111 end | |
| 112 | |
|
999
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
113 % Returns the boundary operator op for the boundary specified by the string boundary. |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
114 % op -- string or a cell array of strings |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
115 % boundary -- string |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
116 function varargout = getBoundaryOperator(obj, op, boundary) |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
117 |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
118 if ~iscell(op) |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
119 op = {op}; |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
120 end |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
121 |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
122 for i = 1:numel(op) |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
123 switch op{i} |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
124 case 'e' |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
125 switch boundary |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
126 case 'l' |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
127 e = obj.e_l; |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
128 case 'r' |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
129 e = obj.e_r; |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
130 otherwise |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
131 error('No such boundary: boundary = %s',boundary); |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
132 end |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
133 varargout{i} = e; |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
134 |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
135 case 'd' |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
136 switch boundary |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
137 case 'l' |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
138 d = obj.d1_l; |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
139 case 'r' |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
140 d = obj.d1_r; |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
141 otherwise |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
142 error('No such boundary: boundary = %s',boundary); |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
143 end |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
144 varargout{i} = d; |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
145 end |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
146 end |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
147 end |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
148 |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
149 % Returns the boundary sign. The right boundary is considered the positive boundary |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
150 % boundary -- string |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
151 function s = getBoundarySign(obj, boundary) |
| 0 | 152 switch boundary |
|
999
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
153 case {'r'} |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
154 s = 1; |
|
337c4d1dcef5
Fix overlooked Schrodinger1d scheme.
Martin Almquist <malmquist@stanford.edu>
parents:
946
diff
changeset
|
155 case {'l'} |
| 0 | 156 s = -1; |
| 157 otherwise | |
| 158 error('No such boundary: boundary = %s',boundary); | |
| 159 end | |
| 160 end | |
| 161 | |
| 162 function N = size(obj) | |
| 163 N = obj.m; | |
| 164 end | |
| 165 | |
| 166 end | |
| 167 | |
| 168 methods(Static) | |
| 169 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u | |
| 170 % and bound_v of scheme schm_v. | |
| 171 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l') | |
| 172 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v) | |
| 173 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v); | |
| 174 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u); | |
| 175 end | |
| 176 end | |
| 177 end |