Mercurial > repos > public > sbplib
annotate +scheme/Schrodinger.m @ 501:b7280c6c6b9a feature/quantumTriangles
Found some small bugs when making slides for pressentation
| author | Ylva Rydin <ylva.rydin@telia.com> |
|---|---|
| date | Tue, 25 Apr 2017 09:52:32 +0200 |
| parents | b91d23271481 |
| children |
| rev | line source |
|---|---|
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65
33f0654a2413
Fixed mistakes in Schrodinger scheme. BC are now working.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
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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 | |
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428
a39fe3bcbd95
Changed so that the shrodinger scheme works with the grids
Ylva Rydin <ylva.rydin@telia.com>
parents:
426
diff
changeset
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7 grid |
|
a39fe3bcbd95
Changed so that the shrodinger scheme works with the grids
Ylva Rydin <ylva.rydin@telia.com>
parents:
426
diff
changeset
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8 |
| 0 | 9 D % non-stabalized scheme operator |
| 10 H % Discrete norm | |
| 11 M % Derivative norm | |
| 12 alpha | |
| 13 | |
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65
33f0654a2413
Fixed mistakes in Schrodinger scheme. BC are now working.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
14 D2 |
| 0 | 15 Hi |
| 16 e_l | |
| 17 e_r | |
| 18 d1_l | |
| 19 d1_r | |
| 20 gamm | |
| 21 end | |
| 22 | |
| 23 methods | |
| 24 % Solving SE in the form u_t = i*u_xx -i*V; | |
|
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b91d23271481
Added new penalty parameter to the interface in shrodinger curve
Ylva Rydin <ylva.rydin@telia.com>
parents:
428
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changeset
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25 function obj = Schrodinger(g,order,V) |
| 0 | 26 default_arg('V',0); |
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b91d23271481
Added new penalty parameter to the interface in shrodinger curve
Ylva Rydin <ylva.rydin@telia.com>
parents:
428
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changeset
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27 obj.grid = g; |
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b91d23271481
Added new penalty parameter to the interface in shrodinger curve
Ylva Rydin <ylva.rydin@telia.com>
parents:
428
diff
changeset
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28 m = N(obj.grid); |
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b91d23271481
Added new penalty parameter to the interface in shrodinger curve
Ylva Rydin <ylva.rydin@telia.com>
parents:
428
diff
changeset
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29 obj.x = points(obj.grid); |
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b91d23271481
Added new penalty parameter to the interface in shrodinger curve
Ylva Rydin <ylva.rydin@telia.com>
parents:
428
diff
changeset
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30 ops = sbp.D2Standard(m,{obj.x(1) obj.x(end)},order); |
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426
29944ea7674b
Updated the Shrodinger scheme to the new operator syntax
Ylva Rydin <ylva.rydin@telia.com>
parents:
67
diff
changeset
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31 |
|
495
b91d23271481
Added new penalty parameter to the interface in shrodinger curve
Ylva Rydin <ylva.rydin@telia.com>
parents:
428
diff
changeset
|
32 |
|
b91d23271481
Added new penalty parameter to the interface in shrodinger curve
Ylva Rydin <ylva.rydin@telia.com>
parents:
428
diff
changeset
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33 obj.h = ops.h; |
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426
29944ea7674b
Updated the Shrodinger scheme to the new operator syntax
Ylva Rydin <ylva.rydin@telia.com>
parents:
67
diff
changeset
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34 obj.D2 = ops.D2; |
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29944ea7674b
Updated the Shrodinger scheme to the new operator syntax
Ylva Rydin <ylva.rydin@telia.com>
parents:
67
diff
changeset
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35 obj.H = ops.H; |
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29944ea7674b
Updated the Shrodinger scheme to the new operator syntax
Ylva Rydin <ylva.rydin@telia.com>
parents:
67
diff
changeset
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36 obj.Hi = ops.HI; |
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29944ea7674b
Updated the Shrodinger scheme to the new operator syntax
Ylva Rydin <ylva.rydin@telia.com>
parents:
67
diff
changeset
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37 obj.M = ops.M; |
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29944ea7674b
Updated the Shrodinger scheme to the new operator syntax
Ylva Rydin <ylva.rydin@telia.com>
parents:
67
diff
changeset
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38 obj.e_l = ops.e_l; |
|
29944ea7674b
Updated the Shrodinger scheme to the new operator syntax
Ylva Rydin <ylva.rydin@telia.com>
parents:
67
diff
changeset
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39 obj.e_r = ops.e_r; |
|
29944ea7674b
Updated the Shrodinger scheme to the new operator syntax
Ylva Rydin <ylva.rydin@telia.com>
parents:
67
diff
changeset
|
40 obj.d1_l = ops.d1_l; |
|
29944ea7674b
Updated the Shrodinger scheme to the new operator syntax
Ylva Rydin <ylva.rydin@telia.com>
parents:
67
diff
changeset
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41 obj.d1_r = ops.d1_r; |
| 0 | 42 |
| 43 | |
| 44 if isa(V,'function_handle') | |
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426
29944ea7674b
Updated the Shrodinger scheme to the new operator syntax
Ylva Rydin <ylva.rydin@telia.com>
parents:
67
diff
changeset
|
45 V_vec = V(obj.x); |
| 0 | 46 else |
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426
29944ea7674b
Updated the Shrodinger scheme to the new operator syntax
Ylva Rydin <ylva.rydin@telia.com>
parents:
67
diff
changeset
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47 V_vec = obj.x*0 + V; |
| 0 | 48 end |
| 49 | |
|
65
33f0654a2413
Fixed mistakes in Schrodinger scheme. BC are now working.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
50 V_mat = spdiags(V_vec,0,m,m); |
| 0 | 51 |
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67
446d67a49cd8
Fixed some errors in scheme.Schrodinger.m
Jonatan Werpers <jonatan@werpers.com>
parents:
65
diff
changeset
|
52 obj.D = 1i * obj.D2 - 1i * V_mat; |
| 0 | 53 |
| 54 obj.m = m; | |
| 55 obj.order = order; | |
| 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 | |
| 70 [e,d,s] = obj.get_boundary_ops(boundary); | |
| 71 | |
| 72 switch type | |
| 73 % Dirichlet boundary condition | |
| 74 case {'D','d','dirichlet'} | |
|
65
33f0654a2413
Fixed mistakes in Schrodinger scheme. BC are now working.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
75 tau = s * 1i*d; |
| 0 | 76 closure = obj.Hi*tau*e'; |
| 77 | |
| 78 switch class(data) | |
| 79 case 'double' | |
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65
33f0654a2413
Fixed mistakes in Schrodinger scheme. BC are now working.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
80 penalty = -obj.Hi*tau*data; |
| 0 | 81 case 'function_handle' |
|
65
33f0654a2413
Fixed mistakes in Schrodinger scheme. BC are now working.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
82 penalty = @(t)-obj.Hi*tau*data(t); |
| 0 | 83 otherwise |
| 84 error('Wierd data argument!') | |
| 85 end | |
| 86 | |
| 87 % Unknown, boundary condition | |
| 88 otherwise | |
| 89 error('No such boundary condition: type = %s',type); | |
| 90 end | |
| 91 end | |
| 92 | |
| 93 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) | |
| 94 % u denotes the solution in the own domain | |
| 95 % v denotes the solution in the neighbour domain | |
| 96 [e_u,d_u,s_u] = obj.get_boundary_ops(boundary); | |
| 97 [e_v,d_v,s_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary); | |
| 98 | |
|
67
446d67a49cd8
Fixed some errors in scheme.Schrodinger.m
Jonatan Werpers <jonatan@werpers.com>
parents:
65
diff
changeset
|
99 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
|
100 b = a'; |
| 0 | 101 |
| 102 tau = b*d_u; | |
|
67
446d67a49cd8
Fixed some errors in scheme.Schrodinger.m
Jonatan Werpers <jonatan@werpers.com>
parents:
65
diff
changeset
|
103 sig = -a*e_u; |
| 0 | 104 |
| 105 closure = obj.Hi * (tau*e_u' + sig*d_u'); | |
| 106 penalty = obj.Hi * (-tau*e_v' - sig*d_v'); | |
| 107 end | |
| 108 | |
| 109 % Ruturns the boundary ops and sign for the boundary specified by the string boundary. | |
| 110 % The right boundary is considered the positive boundary | |
| 111 function [e,d,s] = get_boundary_ops(obj,boundary) | |
| 112 switch boundary | |
| 113 case 'l' | |
| 114 e = obj.e_l; | |
| 115 d = obj.d1_l; | |
| 116 s = -1; | |
| 117 case 'r' | |
| 118 e = obj.e_r; | |
| 119 d = obj.d1_r; | |
| 120 s = 1; | |
| 121 otherwise | |
| 122 error('No such boundary: boundary = %s',boundary); | |
| 123 end | |
| 124 end | |
| 125 | |
| 126 function N = size(obj) | |
| 127 N = obj.m; | |
| 128 end | |
| 129 | |
| 130 end | |
| 131 | |
| 132 methods(Static) | |
| 133 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u | |
| 134 % and bound_v of scheme schm_v. | |
| 135 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l') | |
| 136 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v) | |
| 137 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v); | |
| 138 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u); | |
| 139 end | |
| 140 end | |
| 141 end |