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annotate +scheme/Beam.m @ 577:e45c9b56d50d feature/grids

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Add an Empty grid class The need turned up for the flexural code when we may or may not have a grid for the open water and want to plot that solution. In case there is no open water we need an empty grid to plot the empty gridfunction against to avoid errors.
author Jonatan Werpers <jonatan@werpers.com>
date Thu, 07 Sep 2017 09:16:12 +0200
parents dfb27a7e801f
children 4ced7d47bd1f
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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
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9 h
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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
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19 alphaII
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20 alphaIII
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21
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22 opt
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23 end
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24
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25 methods
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26 function obj = Beam(grid, order, alpha, opsGen, opt)
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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
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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;
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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;
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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;
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69 alphaIII = ops.borrowing.N.S3/2;
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70
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71 obj.gamm = h*alphaII;
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72 obj.delt = h^3*alphaIII;
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73 obj.alphaII = alphaII;
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74 obj.alphaIII = alphaIII;
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75 obj.h = h;
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76 obj.opt = opt;
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77 end
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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
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94 % TODO: Can this be simplifed? Can I handle conditions on u on its own, u_x on its own ...
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95
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96 switch type
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97 case {'dn', 'clamped'} % Dirichlet-neumann boundary condition
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98 alpha = obj.alpha;
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99
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100 % tau1 < -alpha^2/gamma
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101 % tuning = 2;
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102 tuning = 1.1;
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103
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104 tau1 = tuning * alpha/delt;
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105 tau4 = s*alpha;
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106
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107 sig2 = tuning * alpha/gamm;
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108 sig3 = -s*alpha;
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109
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110 tau = tau1*e+tau4*d3;
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111 sig = sig2*d1+sig3*d2;
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112
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113 closure = obj.Hi*(tau*e' + sig*d1');
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114
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115 penalty{1} = -obj.Hi*tau;
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116 penalty{2} = -obj.Hi*sig;
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117
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118
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119 case {'free'}
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120 a = obj.alpha;
339
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121
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122 tau = s*a*d1;
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123 sig = -s*a*e;
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124
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125 closure = obj.Hi*(tau*d2' + sig*d3');
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126 penalty{1} = -obj.Hi*tau;
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127 penalty{1} = -obj.Hi*sig;
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128
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129
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130 otherwise % Unknown, boundary condition
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131 error('No such boundary condition: type = %s',type);
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132 end
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133 end
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134
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135 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary)
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136 % u denotes the solution in the own domain
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137 % v denotes the solution in the neighbour domain
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138 [e_u,d1_u,d2_u,d3_u,s_u] = obj.get_boundary_ops(boundary);
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
139 [e_v,d1_v,d2_v,d3_v,s_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary);
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
140
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
141
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
142 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
143 alpha_v = neighbour_scheme.alpha;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
144
242
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
145
240
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
146 switch boundary
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
147 case 'l'
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
148 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
149 case 'r'
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
150 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
151 end
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
152
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
153
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
154 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
155 gamm_u = obj.gamm;
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
156 delt_u = obj.delt;
175
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
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parents:
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157
240
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
158 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
159 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
160
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
161 tuning = interface_opt.tuning;
175
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
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parents:
diff changeset
162
240
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
163 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
164 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
165 else
242
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
166 h_u = obj.h;
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
167 h_v = neighbour_scheme.h;
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
168
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
169 switch neighbour_boundary
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
170 case 'l'
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
171 neighbour_interface_opt = neighbour_scheme.opt.interface_l;
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
172 case 'r'
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
173 neighbour_interface_opt = neighbour_scheme.opt.interface_r;
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
174 end
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
175
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
176 tau_u = interface_opt.tau;
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
177 sig_u = interface_opt.sig;
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
178 tau_v = neighbour_interface_opt.tau;
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
179 sig_v = neighbour_interface_opt.sig;
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
180
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
181 tau1 = tau_u/h_u^3 + tau_v/h_v^3;
f4306afd6849 Beam: improvements.
Jonatan Werpers <jonatan@werpers.com>
parents: 240
diff changeset
182 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
183 end
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
184
46256fffa329 Added some stuff for default structs. Improved interface for beam.
Jonatan Werpers <jonatan@werpers.com>
parents: 239
diff changeset
185 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
186 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
187 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
188 psi1 = -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
189
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
190 tau = tau1*e_u + tau4*d3_u;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
191 sig = sig2*d1_u + sig3*d2_u ;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
192 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
193 psi = psi1*e_u ;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
194
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
195 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
196 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
197 end
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
198
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
199 % 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:
diff changeset
200 % 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
201 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
202 switch boundary
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
203 case 'l'
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
204 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
205 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
206 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
207 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
208 s = -1;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
209 case 'r'
176
d095b5396103 Fixed some bugs in Beam schemes.
Jonatan Werpers <jonatan@werpers.com>
parents: 175
diff changeset
210 e = obj.e_r;
d095b5396103 Fixed some bugs in Beam schemes.
Jonatan Werpers <jonatan@werpers.com>
parents: 175
diff changeset
211 d1 = obj.d1_r;
d095b5396103 Fixed some bugs in Beam schemes.
Jonatan Werpers <jonatan@werpers.com>
parents: 175
diff changeset
212 d2 = obj.d2_r;
d095b5396103 Fixed some bugs in Beam schemes.
Jonatan Werpers <jonatan@werpers.com>
parents: 175
diff changeset
213 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
214 s = 1;
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
215 otherwise
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
216 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
217 end
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
218 end
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
219
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
220 function N = size(obj)
224
05304d7792dc Fixed type in scheme.Beam
Jonatan Werpers <jonatan@werpers.com>
parents: 223
diff changeset
221 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
222 end
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
223
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
224 end
8f22829b69d0 Added and upgraded schemes for the beam equation in 1d and 2d.
Jonatan Werpers <jonatan@werpers.com>
parents:
diff changeset
225 end