Mercurial > repos > public > sbplib
annotate +scheme/Laplace1D.m @ 896:09c5fbc783d3
Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
| author | Jonatan Werpers <jonatan@werpers.com> |
|---|---|
| date | Thu, 22 Nov 2018 07:58:11 +0100 |
| parents | +scheme/Wave.m@cb2b12246b7e |
| children | bd79326ebcd0 |
| rev | line source |
|---|---|
|
896
09c5fbc783d3
Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
Jonatan Werpers <jonatan@werpers.com>
parents:
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diff
changeset
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1 classdef Laplace1D < scheme.Scheme |
| 0 | 2 properties |
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Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
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3 g |
| 0 | 4 order % Order accuracy for the approximation |
| 5 | |
| 6 D % non-stabalized scheme operator | |
| 7 H % Discrete norm | |
| 8 M % Derivative norm | |
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Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
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9 a |
| 0 | 10 |
| 11 D2 | |
| 12 Hi | |
| 13 e_l | |
| 14 e_r | |
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Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
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parents:
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15 d_l |
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Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
Jonatan Werpers <jonatan@werpers.com>
parents:
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16 d_r |
| 0 | 17 gamm |
| 18 end | |
| 19 | |
| 20 methods | |
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896
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Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
Jonatan Werpers <jonatan@werpers.com>
parents:
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21 function obj = Laplace1D(g, order, a) |
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Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
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parents:
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22 default_arg('a', 1); |
| 0 | 23 |
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Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
Jonatan Werpers <jonatan@werpers.com>
parents:
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24 assertType(g, 'grid.Cartesian'); |
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Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
Jonatan Werpers <jonatan@werpers.com>
parents:
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25 |
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Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
Jonatan Werpers <jonatan@werpers.com>
parents:
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26 ops = sbp.Ordinary(g.size(), g.h, order); |
| 0 | 27 |
| 28 obj.D2 = sparse(ops.derivatives.D2); | |
| 29 obj.H = sparse(ops.norms.H); | |
| 30 obj.Hi = sparse(ops.norms.HI); | |
| 31 obj.M = sparse(ops.norms.M); | |
| 32 obj.e_l = sparse(ops.boundary.e_1); | |
| 33 obj.e_r = sparse(ops.boundary.e_m); | |
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Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
Jonatan Werpers <jonatan@werpers.com>
parents:
141
diff
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34 obj.d_l = sparse(ops.boundary.S_1); |
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Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
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parents:
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35 obj.d_r = sparse(ops.boundary.S_m); |
| 0 | 36 |
| 37 | |
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Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
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parents:
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38 obj.g = g; |
| 0 | 39 obj.order = order; |
| 40 | |
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parents:
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41 obj.a = a; |
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Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
Jonatan Werpers <jonatan@werpers.com>
parents:
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diff
changeset
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42 obj.D = a*obj.D2; |
| 0 | 43 |
| 44 obj.gamm = h*ops.borrowing.M.S; | |
| 45 end | |
| 46 | |
| 47 | |
| 48 % Closure functions return the opertors applied to the own doamin to close the boundary | |
| 49 % Penalty functions return the opertors to force the solution. In the case of an interface it returns the operator applied to the other doamin. | |
| 50 % boundary is a string specifying the boundary e.g. 'l','r' or 'e','w','n','s'. | |
| 51 % type is a string specifying the type of boundary condition if there are several. | |
| 52 % data is a function returning the data that should be applied at the boundary. | |
| 53 % neighbour_scheme is an instance of Scheme that should be interfaced to. | |
| 54 % neighbour_boundary is a string specifying which boundary to interface to. | |
| 55 function [closure, penalty] = boundary_condition(obj,boundary,type,data) | |
| 56 default_arg('type','neumann'); | |
| 57 default_arg('data',0); | |
| 58 | |
| 59 [e,d,s] = obj.get_boundary_ops(boundary); | |
| 60 | |
| 61 switch type | |
| 62 % Dirichlet boundary condition | |
| 63 case {'D','dirichlet'} | |
| 64 alpha = obj.alpha; | |
| 65 | |
| 66 % tau1 < -alpha^2/gamma | |
| 67 tuning = 1.1; | |
| 68 tau1 = -tuning*alpha/obj.gamm; | |
| 69 tau2 = s*alpha; | |
| 70 | |
| 71 p = tau1*e + tau2*d; | |
| 72 | |
| 73 closure = obj.Hi*p*e'; | |
| 74 | |
| 75 pp = obj.Hi*p; | |
| 76 switch class(data) | |
| 77 case 'double' | |
| 78 penalty = pp*data; | |
| 79 case 'function_handle' | |
| 80 penalty = @(t)pp*data(t); | |
| 81 otherwise | |
| 82 error('Wierd data argument!') | |
| 83 end | |
| 84 | |
| 85 | |
| 86 % Neumann boundary condition | |
| 87 case {'N','neumann'} | |
| 88 alpha = obj.alpha; | |
| 89 tau1 = -s*alpha; | |
| 90 tau2 = 0; | |
| 91 tau = tau1*e + tau2*d; | |
| 92 | |
| 93 closure = obj.Hi*tau*d'; | |
| 94 | |
| 95 pp = obj.Hi*tau; | |
| 96 switch class(data) | |
| 97 case 'double' | |
| 98 penalty = pp*data; | |
| 99 case 'function_handle' | |
| 100 penalty = @(t)pp*data(t); | |
| 101 otherwise | |
| 102 error('Wierd data argument!') | |
| 103 end | |
| 104 | |
| 105 % Unknown, boundary condition | |
| 106 otherwise | |
| 107 error('No such boundary condition: type = %s',type); | |
| 108 end | |
| 109 end | |
| 110 | |
| 111 function [closure, penalty] = interface(obj,boundary,neighbour_scheme,neighbour_boundary) | |
| 112 % u denotes the solution in the own domain | |
| 113 % v denotes the solution in the neighbour domain | |
| 114 [e_u,d_u,s_u] = obj.get_boundary_ops(boundary); | |
| 115 [e_v,d_v,s_v] = neighbour_scheme.get_boundary_ops(neighbour_boundary); | |
| 116 | |
| 117 tuning = 1.1; | |
| 118 | |
| 119 alpha_u = obj.alpha; | |
| 120 alpha_v = neighbour_scheme.alpha; | |
| 121 | |
| 122 gamm_u = obj.gamm; | |
| 123 gamm_v = neighbour_scheme.gamm; | |
| 124 | |
| 125 % tau1 < -(alpha_u/gamm_u + alpha_v/gamm_v) | |
| 126 | |
| 127 tau1 = -(alpha_u/gamm_u + alpha_v/gamm_v) * tuning; | |
| 128 tau2 = s_u*1/2*alpha_u; | |
| 129 sig1 = s_u*(-1/2); | |
| 130 sig2 = 0; | |
| 131 | |
| 132 tau = tau1*e_u + tau2*d_u; | |
| 133 sig = sig1*e_u + sig2*d_u; | |
| 134 | |
| 135 closure = obj.Hi*( tau*e_u' + sig*alpha_u*d_u'); | |
| 136 penalty = obj.Hi*(-tau*e_v' - sig*alpha_v*d_v'); | |
| 137 end | |
| 138 | |
| 139 % Ruturns the boundary ops and sign for the boundary specified by the string boundary. | |
| 140 % The right boundary is considered the positive boundary | |
| 141 function [e,d,s] = get_boundary_ops(obj,boundary) | |
| 142 switch boundary | |
| 143 case 'l' | |
| 144 e = obj.e_l; | |
|
896
09c5fbc783d3
Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
Jonatan Werpers <jonatan@werpers.com>
parents:
141
diff
changeset
|
145 d = obj.d_l; |
| 0 | 146 s = -1; |
| 147 case 'r' | |
| 148 e = obj.e_r; | |
|
896
09c5fbc783d3
Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
Jonatan Werpers <jonatan@werpers.com>
parents:
141
diff
changeset
|
149 d = obj.d_r; |
| 0 | 150 s = 1; |
| 151 otherwise | |
| 152 error('No such boundary: boundary = %s',boundary); | |
| 153 end | |
| 154 end | |
| 155 | |
| 156 function N = size(obj) | |
| 157 N = obj.m; | |
| 158 end | |
| 159 | |
| 160 end | |
| 161 | |
| 162 methods(Static) | |
| 163 % Calculates the matrcis need for the inteface coupling between boundary bound_u of scheme schm_u | |
| 164 % and bound_v of scheme schm_v. | |
| 165 % [uu, uv, vv, vu] = inteface_couplong(A,'r',B,'l') | |
| 166 function [uu, uv, vv, vu] = interface_coupling(schm_u,bound_u,schm_v,bound_v) | |
| 167 [uu,uv] = schm_u.interface(bound_u,schm_v,bound_v); | |
| 168 [vv,vu] = schm_v.interface(bound_v,schm_u,bound_u); | |
| 169 end | |
| 170 end | |
| 171 end |