Mercurial > repos > public > sbplib
annotate +scheme/Schrodinger.m @ 1347:ac54767ae1fb feature/poroelastic tip
Add interface, not fully compatible.
| author | Martin Almquist <martin.almquist@it.uu.se> |
|---|---|
| date | Tue, 30 Apr 2024 14:58:35 +0200 |
| parents | 706d1c2b4199 |
| children | 337c4d1dcef5 c12b84fe9b00 |
| 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 | |
| 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' | |
|
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 | |
|
946
706d1c2b4199
Raname opts to type in a bunch of interface methods
Jonatan Werpers <jonatan@werpers.com>
parents:
910
diff
changeset
|
93 function [closure, penalty] = interface(obj, boundary, neighbour_scheme, neighbour_boundary, type) |
| 0 | 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 |