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

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Initial commit.
author Jonatan Werpers <jonatan@werpers.com>
date Thu, 17 Sep 2015 10:12:50 +0200
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children d52e5cdb6eff
comparison
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-1:000000000000 0:48b6fb693025
1 classdef SchmWave < 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 D2
14 Hi
15 e_l
16 e_r
17 d1_l
18 d1_r
19 gamm
20 end
21
22 methods
23 function obj = SchmWave(m,xlim,order,alpha)
24 default_arg('a',1);
25 [x, h] = util.get_grid(xlim{:},m);
26
27 ops = sbp.Ordinary(m,h,order);
28
29 obj.D2 = sparse(ops.derivatives.D2);
30 obj.H = sparse(ops.norms.H);
31 obj.Hi = sparse(ops.norms.HI);
32 obj.M = sparse(ops.norms.M);
33 obj.e_l = sparse(ops.boundary.e_1);
34 obj.e_r = sparse(ops.boundary.e_m);
35 obj.d1_l = sparse(ops.boundary.S_1);
36 obj.d1_r = sparse(ops.boundary.S_m);
37
38
39 obj.m = m;
40 obj.h = h;
41 obj.order = order;
42
43 obj.alpha = alpha;
44 obj.D = alpha*obj.D2;
45 obj.x = x;
46
47 obj.gamm = h*ops.borrowing.M.S;
48
49 end
50
51
52 % Closure functions return the opertors applied to the own doamin to close the boundary
53 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
54 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
55 % type is a string specifying the type of boundary condition if there are several.
56 % data is a function returning the data that should be applied at the boundary.
57 % neighbour_scheme is an instance of Scheme that should be interfaced to.
58 % neighbour_boundary is a string specifying which boundary to interface to.
59 function [closure, penalty] = boundary_condition(obj,boundary,type,data)
60 default_arg('type','neumann');
61 default_arg('data',0);
62
63 [e,d,s] = obj.get_boundary_ops(boundary);
64
65 switch type
66 % Dirichlet boundary condition
67 case {'D','dirichlet'}
68 alpha = obj.alpha;
69
70 % tau1 < -alpha^2/gamma
71 tuning = 1.1;
72 tau1 = -tuning*alpha/obj.gamm;
73 tau2 = s*alpha;
74
75 p = tau1*e + tau2*d;
76
77 closure = obj.Hi*p*e';
78
79 pp = obj.Hi*p;
80 switch class(data)
81 case 'double'
82 penalty = pp*data;
83 case 'function_handle'
84 penalty = @(t)pp*data(t);
85 otherwise
86 error('Wierd data argument!')
87 end
88
89
90 % Neumann boundary condition
91 case {'N','neumann'}
92 alpha = obj.alpha;
93 tau1 = -s*alpha;
94 tau2 = 0;
95 tau = tau1*e + tau2*d;
96
97 closure = obj.Hi*tau*d';
98
99 pp = obj.Hi*tau;
100 switch class(data)
101 case 'double'
102 penalty = pp*data;
103 case 'function_handle'
104 penalty = @(t)pp*data(t);
105 otherwise
106 error('Wierd data argument!')
107 end
108
109 % Unknown, boundary condition
110 otherwise
111 error('No such boundary condition: type = %s',type);
112 end
113 end
114
115 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
116 % u denotes the solution in the own domain
117 % v denotes the solution in the neighbour domain
118 [e_u,d_u,s_u] = obj.get_boundary_ops(boundary);
119 [e_v,d_v,s_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
120
121 tuning = 1.1;
122
123 alpha_u = obj.alpha;
124 alpha_v = neighbour_scheme.alpha;
125
126 gamm_u = obj.gamm;
127 gamm_v = neighbour_scheme.gamm;
128
129 % tau1 < -(alpha_u/gamm_u + alpha_v/gamm_v)
130
131 tau1 = -(alpha_u/gamm_u + alpha_v/gamm_v) * tuning;
132 tau2 = s_u*1/2*alpha_u;
133 sig1 = s_u*(-1/2);
134 sig2 = 0;
135
136 tau = tau1*e_u + tau2*d_u;
137 sig = sig1*e_u + sig2*d_u;
138
139 closure = obj.Hi*( tau*e_u' + sig*alpha_u*d_u');
140 penalty = obj.Hi*(-tau*e_v' - sig*alpha_v*d_v');
141 end
142
143 % Ruturns the boundary ops and sign for the boundary specified by the string boundary.
144 % The right boundary is considered the positive boundary
145 function [e,d,s] = get_boundary_ops(obj,boundary)
146 switch boundary
147 case 'l'
148 e = obj.e_l;
149 d = obj.d1_l;
150 s = -1;
151 case 'r'
152 e = obj.e_r;
153 d = obj.d1_r;
154 s = 1;
155 otherwise
156 error('No such boundary: boundary = %s',boundary);
157 end
158 end
159
160 function N = size(obj)
161 N = obj.m;
162 end
163
164 end
165
166 methods(Static)
167 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u
168 % and bound_v of scheme schm_v.
169 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l')
170 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v)
171 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v);
172 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u);
173 end
174 end
175 end