Mercurial > repos > public > sbplib
annotate +scheme/Wave.m @ 319:fc91e3a2d44a feature/beams
Cleaned d4_variable_6_min_boundary_points.
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Mon, 26 Sep 2016 08:52:03 +0200 |
| parents | cb2b12246b7e |
| children | 459eeb99130f |
| rev | line source |
|---|---|
|
141
cb2b12246b7e
Fixed path to some superclasses.
Jonatan Werpers <jonatan@werpers.com>
parents:
125
diff
changeset
|
1 classdef Wave < 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 | |
| 13 D2 | |
| 14 Hi | |
| 15 e_l | |
| 16 e_r | |
| 17 d1_l | |
| 18 d1_r | |
| 19 gamm | |
| 20 end | |
| 21 | |
| 22 methods | |
|
125
d52e5cdb6eff
Fixed some class name, file name errors.
Jonatan Werpers <jonatan@werpers.com>
parents:
0
diff
changeset
|
23 function obj = Wave(m,xlim,order,alpha) |
| 0 | 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 |