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annotate +scheme/Beam.m @ 339:3135e13ae509 feature/beams

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Implemented free BC. Not tested yet.
author Jonatan Werpers <jonatan@werpers.com>
date Mon, 24 Oct 2016 17:01:34 +0200
parents bf801c3709be
children 25ae8333ce2b
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175
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1 classdef Beam < scheme.Scheme
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2 properties
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3 order % Order accuracy for the approximation
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4 grid
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5
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6 D % non-stabalized scheme operator
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7 alpha
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8
242
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9 h
175
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10 H % Discrete norm
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11 Hi
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12
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13 e_l, e_r
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14 d1_l, d1_r
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15 d2_l, d2_r
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16 d3_l, d3_r
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17 gamm
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18 delt
242
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19 alphaII
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20 alphaIII
240
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21
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22 opt
175
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23 end
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24
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25 methods
240
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26 function obj = Beam(grid, order, alpha, opsGen, opt)
236
8592358a3935 Beam: Added tuning as a parameter to contructor.
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27 default_arg('alpha', -1);
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28
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29 % default_arg('opsGen', @sbp.D4);
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30 default_arg('opsGen', @sbp.D4Variable); % Supposed to be better
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31
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32 opt_default.interface_l.tuning = 1.1;
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33 opt_default.interface_l.tau = [];
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34 opt_default.interface_l.sig = [];
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35 opt_default.interface_r.tuning = 1.1;
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36 opt_default.interface_r.tau = [];
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37 opt_default.interface_r.sig = [];
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38 default_struct('opt', opt_default);
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39
176
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40 if ~isa(grid, 'grid.Cartesian') || grid.D() ~= 1
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41 error('Grid must be 1d cartesian');
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42 end
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43
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44 obj.grid = grid;
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45 obj.order = order;
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46 obj.alpha = alpha;
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47
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48 m = grid.m;
176
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49 h = grid.scaling();
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50
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51 x_lim = {grid.x{1}(1), grid.x{1}(end)};
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52 ops = opsGen(m, x_lim, order);
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53
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54 D4 = ops.D4;
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55 obj.H = ops.H;
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56 obj.Hi = ops.HI;
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57 obj.e_l = ops.e_l;
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58 obj.e_r = ops.e_r;
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59 obj.d1_l = ops.d1_l;
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60 obj.d1_r = ops.d1_r;
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61 obj.d2_l = ops.d2_l;
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62 obj.d2_r = ops.d2_r;
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63 obj.d3_l = ops.d3_l;
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64 obj.d3_r = ops.d3_r;
175
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65
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66 obj.D = alpha*D4;
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67
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68 alphaII = ops.borrowing.N.S2/2;
240
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69 alphaIII = ops.borrowing.N.S3/2;
239
ba56e0d621f2 Beam: Added ability to pick alphaII and alphaIII to control tau and sigma.
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70
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71 obj.gamm = h*alphaII;
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72 obj.delt = h^3*alphaIII;
242
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73 obj.alphaII = alphaII;
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74 obj.alphaIII = alphaIII;
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75 obj.h = h;
240
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76 obj.opt = opt;
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77 end
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78
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79
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80 % Closure functions return the opertors applied to the own doamin to close the boundary
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81 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin.
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82 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'.
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83 % type is a string specifying the type of boundary condition if there are several.
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84 % neighbour_scheme is an instance of Scheme that should be interfaced to.
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85 % neighbour_boundary is a string specifying which boundary to interface to.
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86 function [closure, penalty] = boundary_condition(obj,boundary,type)
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87 default_arg('type','dn');
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88
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89 [e, d1, d2, d3, s] = obj.get_boundary_ops(boundary);
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90 gamm = obj.gamm;
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91 delt = obj.delt;
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92
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93 switch type
339
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94 case {'dn', 'clamped'} % Dirichlet-neumann boundary condition
175
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95 alpha = obj.alpha;
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96
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97 % tau1 < -alpha^2/gamma
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98 % tuning = 2;
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99 tuning = 1.1;
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100
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101 tau1 = tuning * alpha/delt;
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102 tau4 = s*alpha;
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103
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104 sig2 = tuning * alpha/gamm;
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105 sig3 = -s*alpha;
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106
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107 tau = tau1*e+tau4*d3;
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108 sig = sig2*d1+sig3*d2;
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109
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110 closure = obj.Hi*(tau*e' + sig*d1');
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111
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112 penalty{1} = -obj.Hi*tau;
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113 penalty{2} = -obj.Hi*sig;
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114
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115
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116 case {'free'}
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117 a = -obj.alpha;
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118
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119 tau = s*a*d1;
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120 sig = -s*a*e;
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121
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122 closure = obj.Hi*(tau*d2' + sig*d3');
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123 penalty{1} = -obj.Hi*tau;
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124 penalty{1} = -obj.Hi*sig;
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125
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126
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127 otherwise % Unknown, boundary condition
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128 error('No such boundary condition: type = %s',type);
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129 end
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130 end
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131
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132 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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133 % u denotes the solution in the own domain
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134 % v denotes the solution in the neighbour domain
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135 [e_u,d1_u,d2_u,d3_u,s_u] = obj.get_boundary_ops(boundary);
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136 [e_v,d1_v,d2_v,d3_v,s_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
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137
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138
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
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diff changeset
139 alpha_u = obj.alpha;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
140 alpha_v = neighbour_scheme.alpha;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
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parents:
diff changeset
141
242
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
142
240
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
143 switch boundary
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
144 case 'l'
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
145 interface_opt = obj.opt.interface_l;
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
146 case 'r'
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
147 interface_opt = obj.opt.interface_r;
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
148 end
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
149
46256fffa329 Added some stuff for default structs. Improved interface for beam.
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parents: 239
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150
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
151 if isempty(interface_opt.tau) && isempty(interface_opt.sig)
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
152 gamm_u = obj.gamm;
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
153 delt_u = obj.delt;
175
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
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154
240
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
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diff changeset
155 gamm_v = neighbour_scheme.gamm;
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
156 delt_v = neighbour_scheme.delt;
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
157
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
158 tuning = interface_opt.tuning;
175
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
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159
240
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
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diff changeset
160 tau1 = ((alpha_u/2)/delt_u + (alpha_v/2)/delt_v)/2*tuning;
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
161 sig2 = ((alpha_u/2)/gamm_u + (alpha_v/2)/gamm_v)/2*tuning;
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
162 else
242
f4306afd6849 Beam: improvements.
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163 h_u = obj.h;
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
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164 h_v = neighbour_scheme.h;
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
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165
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
166 switch neighbour_boundary
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
167 case 'l'
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
168 neighbour_interface_opt = neighbour_scheme.opt.interface_l;
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
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diff changeset
169 case 'r'
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
170 neighbour_interface_opt = neighbour_scheme.opt.interface_r;
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
171 end
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
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diff changeset
172
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
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diff changeset
173 tau_u = interface_opt.tau;
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
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174 sig_u = interface_opt.sig;
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
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diff changeset
175 tau_v = neighbour_interface_opt.tau;
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
176 sig_v = neighbour_interface_opt.sig;
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
177
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
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diff changeset
178 tau1 = tau_u/h_u^3 + tau_v/h_v^3;
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
179 sig2 = sig_u/h_u + sig_v/h_v;
240
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
180 end
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
181
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
182 tau4 = s_u*alpha_u/2;
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
183 sig3 = -s_u*alpha_u/2;
175
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
184 phi2 = s_u*1/2;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
185 psi1 = -s_u*1/2;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
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parents:
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186
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
187 tau = tau1*e_u + tau4*d3_u;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
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parents:
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188 sig = sig2*d1_u + sig3*d2_u ;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
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parents:
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189 phi = phi2*d1_u ;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
190 psi = psi1*e_u ;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
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191
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
192 closure = obj.Hi*(tau*e_u' + sig*d1_u' + phi*alpha_u*d2_u' + psi*alpha_u*d3_u');
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
193 penalty = -obj.Hi*(tau*e_v' + sig*d1_v' + phi*alpha_v*d2_v' + psi*alpha_v*d3_v');
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
194 end
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
195
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
196 % Returns the boundary ops and sign for the boundary specified by the string boundary.
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
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197 % The right boundary is considered the positive boundary
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
198 function [e, d1, d2, d3, s] = get_boundary_ops(obj,boundary)
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
199 switch boundary
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
200 case 'l'
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
201 e = obj.e_l;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
202 d1 = obj.d1_l;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
203 d2 = obj.d2_l;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
204 d3 = obj.d3_l;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
205 s = -1;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
206 case 'r'
176
d095b5396103 Fixed some bugs in Beam schemes.
Jonatan Werpers <jonatan@werpers.com>
parents: 175
diff changeset
207 e = obj.e_r;
d095b5396103 Fixed some bugs in Beam schemes.
Jonatan Werpers <jonatan@werpers.com>
parents: 175
diff changeset
208 d1 = obj.d1_r;
d095b5396103 Fixed some bugs in Beam schemes.
Jonatan Werpers <jonatan@werpers.com>
parents: 175
diff changeset
209 d2 = obj.d2_r;
d095b5396103 Fixed some bugs in Beam schemes.
Jonatan Werpers <jonatan@werpers.com>
parents: 175
diff changeset
210 d3 = obj.d3_r;
175
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
211 s = 1;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
212 otherwise
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
213 error('No such boundary: boundary = %s',boundary);
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
214 end
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
215 end
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
216
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
217 function N = size(obj)
224
05304d7792dc Fixed type in scheme.Beam
Jonatan Werpers <jonatan@werpers.com>
parents: 223
diff changeset
218 N = obj.grid.N;
175
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
219 end
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
220
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
221 end
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
222 end