Mercurial > repos > public > sbplib
annotate +scheme/Laplace1d.m @ 1301:8978521b0f06 default
Fix incorrect package name.
| author | Vidar Stiernström <vidar.stiernstrom@it.uu.se> |
|---|---|
| date | Wed, 08 Jul 2020 19:11:04 +0200 |
| parents | 33c378e508d2 |
| children |
| rev | line source |
|---|---|
|
950
cab047de7f5d
Rename *2D schemes to *2d
Jonatan Werpers <jonatan@werpers.com>
parents:
946
diff
changeset
|
1 classdef Laplace1d < scheme.Scheme |
| 0 | 2 properties |
| 898 | 3 grid |
| 0 | 4 order % Order accuracy for the approximation |
| 5 | |
| 6 D % non-stabalized scheme operator | |
| 7 H % Discrete norm | |
| 8 M % Derivative norm | |
|
896
09c5fbc783d3
Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
Jonatan Werpers <jonatan@werpers.com>
parents:
141
diff
changeset
|
9 a |
| 0 | 10 |
| 11 D2 | |
| 12 Hi | |
| 13 e_l | |
| 14 e_r | |
|
896
09c5fbc783d3
Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
Jonatan Werpers <jonatan@werpers.com>
parents:
141
diff
changeset
|
15 d_l |
|
09c5fbc783d3
Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
Jonatan Werpers <jonatan@werpers.com>
parents:
141
diff
changeset
|
16 d_r |
| 0 | 17 gamm |
| 18 end | |
| 19 | |
| 20 methods | |
|
950
cab047de7f5d
Rename *2D schemes to *2d
Jonatan Werpers <jonatan@werpers.com>
parents:
946
diff
changeset
|
21 function obj = Laplace1d(grid, order, a) |
|
896
09c5fbc783d3
Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
Jonatan Werpers <jonatan@werpers.com>
parents:
141
diff
changeset
|
22 default_arg('a', 1); |
| 0 | 23 |
| 898 | 24 assertType(grid, 'grid.Cartesian'); |
|
896
09c5fbc783d3
Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
Jonatan Werpers <jonatan@werpers.com>
parents:
141
diff
changeset
|
25 |
| 898 | 26 ops = sbp.D2Standard(grid.size(), grid.lim{1}, order); |
| 0 | 27 |
| 898 | 28 obj.D2 = sparse(ops.D2); |
| 29 obj.H = sparse(ops.H); | |
| 30 obj.Hi = sparse(ops.HI); | |
| 31 obj.M = sparse(ops.M); | |
| 32 obj.e_l = sparse(ops.e_l); | |
| 33 obj.e_r = sparse(ops.e_r); | |
| 34 obj.d_l = -sparse(ops.d1_l); | |
| 35 obj.d_r = sparse(ops.d1_r); | |
| 0 | 36 |
| 37 | |
| 898 | 38 obj.grid = grid; |
| 0 | 39 obj.order = order; |
| 40 | |
|
896
09c5fbc783d3
Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
Jonatan Werpers <jonatan@werpers.com>
parents:
141
diff
changeset
|
41 obj.a = a; |
|
09c5fbc783d3
Rename and mordernize scheme.Wave to scheme.Laplace1d. Not fully converted
Jonatan Werpers <jonatan@werpers.com>
parents:
141
diff
changeset
|
42 obj.D = a*obj.D2; |
| 0 | 43 |
| 898 | 44 obj.gamm = grid.h*ops.borrowing.M.S; |
| 0 | 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 | |
|
1045
dc1bcbef2a86
Remove ability to get several boundary ops at the same time from a few of the schemes
Jonatan Werpers <jonatan@werpers.com>
parents:
1044
diff
changeset
|
59 e = obj.getBoundaryOperator('e', boundary); |
|
dc1bcbef2a86
Remove ability to get several boundary ops at the same time from a few of the schemes
Jonatan Werpers <jonatan@werpers.com>
parents:
1044
diff
changeset
|
60 d = obj.getBoundaryOperator('d', boundary); |
|
998
2b1b944deae1
Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
Martin Almquist <malmquist@stanford.edu>
parents:
950
diff
changeset
|
61 s = obj.getBoundarySign(boundary); |
| 0 | 62 |
| 63 switch type | |
| 64 % Dirichlet boundary condition | |
|
1082
a20fc67e9ac0
Add d and n as acceptable boundary condition identifiers, which is consistent with eg LaplaceCurvilinear.
Martin Almquist <malmquist@stanford.edu>
parents:
1079
diff
changeset
|
65 case {'D','d','dirichlet'} |
| 0 | 66 tuning = 1.1; |
| 898 | 67 tau1 = -tuning/obj.gamm; |
| 68 tau2 = 1; | |
| 0 | 69 |
| 898 | 70 tau = tau1*e + tau2*d; |
| 0 | 71 |
| 898 | 72 closure = obj.a*obj.Hi*tau*e'; |
|
1116
33c378e508d2
Bugfix minus sign in Laplace1d Dirichlet penalty.
Martin Almquist <malmquist@stanford.edu>
parents:
1083
diff
changeset
|
73 penalty = -obj.a*obj.Hi*tau; |
| 0 | 74 |
| 75 % Neumann boundary condition | |
|
1082
a20fc67e9ac0
Add d and n as acceptable boundary condition identifiers, which is consistent with eg LaplaceCurvilinear.
Martin Almquist <malmquist@stanford.edu>
parents:
1079
diff
changeset
|
76 case {'N','n','neumann'} |
| 898 | 77 tau = -e; |
| 0 | 78 |
| 898 | 79 closure = obj.a*obj.Hi*tau*d'; |
| 80 penalty = -obj.a*obj.Hi*tau; | |
| 0 | 81 |
| 82 % Unknown, boundary condition | |
| 83 otherwise | |
| 84 error('No such boundary condition: type = %s',type); | |
| 85 end | |
| 86 end | |
| 87 | |
|
946
706d1c2b4199
Raname opts to type in a bunch of interface methods
Jonatan Werpers <jonatan@werpers.com>
parents:
943
diff
changeset
|
88 function [closure, penalty] = interface(obj, boundary, neighbour_scheme, neighbour_boundary, type) |
| 0 | 89 % u denotes the solution in the own domain |
| 90 % v denotes the solution in the neighbour domain | |
|
1047
6bc55a773e7c
Fix some mistakes from dc1bcbef2a86
Jonatan Werpers <jonatan@werpers.com>
parents:
1046
diff
changeset
|
91 e_u = obj.getBoundaryOperator('e', boundary); |
|
6bc55a773e7c
Fix some mistakes from dc1bcbef2a86
Jonatan Werpers <jonatan@werpers.com>
parents:
1046
diff
changeset
|
92 d_u = obj.getBoundaryOperator('d', boundary); |
|
998
2b1b944deae1
Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
Martin Almquist <malmquist@stanford.edu>
parents:
950
diff
changeset
|
93 s_u = obj.getBoundarySign(boundary); |
| 898 | 94 |
|
1047
6bc55a773e7c
Fix some mistakes from dc1bcbef2a86
Jonatan Werpers <jonatan@werpers.com>
parents:
1046
diff
changeset
|
95 e_v = neighbour_scheme.getBoundaryOperator('e', neighbour_boundary); |
|
6bc55a773e7c
Fix some mistakes from dc1bcbef2a86
Jonatan Werpers <jonatan@werpers.com>
parents:
1046
diff
changeset
|
96 d_v = neighbour_scheme.getBoundaryOperator('d', neighbour_boundary); |
|
998
2b1b944deae1
Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
Martin Almquist <malmquist@stanford.edu>
parents:
950
diff
changeset
|
97 s_v = neighbour_scheme.getBoundarySign(neighbour_boundary); |
| 0 | 98 |
| 898 | 99 a_u = obj.a; |
| 100 a_v = neighbour_scheme.a; | |
| 0 | 101 |
| 102 gamm_u = obj.gamm; | |
| 103 gamm_v = neighbour_scheme.gamm; | |
| 104 | |
| 898 | 105 tuning = 1.1; |
|
946
706d1c2b4199
Raname opts to type in a bunch of interface methods
Jonatan Werpers <jonatan@werpers.com>
parents:
943
diff
changeset
|
106 |
|
1083
a22b23098021
Divide interface penalty strength by 4, to make it sharp. Stability verified by eigenvalue computations.
Martin Almquist <malmquist@stanford.edu>
parents:
1082
diff
changeset
|
107 tau1 = -1/4*(a_u/gamm_u + a_v/gamm_v) * tuning; |
| 898 | 108 tau2 = 1/2*a_u; |
| 109 sig1 = -1/2; | |
| 0 | 110 sig2 = 0; |
| 111 | |
| 112 tau = tau1*e_u + tau2*d_u; | |
| 113 sig = sig1*e_u + sig2*d_u; | |
| 114 | |
| 898 | 115 closure = obj.Hi*( tau*e_u' + sig*a_u*d_u'); |
| 116 penalty = obj.Hi*(-tau*e_v' + sig*a_v*d_v'); | |
| 0 | 117 end |
| 118 | |
|
998
2b1b944deae1
Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
Martin Almquist <malmquist@stanford.edu>
parents:
950
diff
changeset
|
119 % Returns the boundary operator op for the boundary specified by the string boundary. |
|
1045
dc1bcbef2a86
Remove ability to get several boundary ops at the same time from a few of the schemes
Jonatan Werpers <jonatan@werpers.com>
parents:
1044
diff
changeset
|
120 % op -- string |
|
998
2b1b944deae1
Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
Martin Almquist <malmquist@stanford.edu>
parents:
950
diff
changeset
|
121 % boundary -- string |
|
1045
dc1bcbef2a86
Remove ability to get several boundary ops at the same time from a few of the schemes
Jonatan Werpers <jonatan@werpers.com>
parents:
1044
diff
changeset
|
122 function o = getBoundaryOperator(obj, op, boundary) |
|
1046
19ed046aec52
Clean up getBoundaryOps for a few schemes
Jonatan Werpers <jonatan@werpers.com>
parents:
1045
diff
changeset
|
123 assertIsMember(op, {'e', 'd'}) |
|
1042
8d73fcdb07a5
Add asserts to boundary identifier inputs
Jonatan Werpers <jonatan@werpers.com>
parents:
998
diff
changeset
|
124 assertIsMember(boundary, {'l', 'r'}) |
|
998
2b1b944deae1
Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
Martin Almquist <malmquist@stanford.edu>
parents:
950
diff
changeset
|
125 |
|
1079
ae4b090b5299
Bugfix missing semi-colon in Laplace1d.
Martin Almquist <malmquist@stanford.edu>
parents:
1049
diff
changeset
|
126 o = obj.([op, '_', boundary]); |
|
998
2b1b944deae1
Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
Martin Almquist <malmquist@stanford.edu>
parents:
950
diff
changeset
|
127 end |
|
2b1b944deae1
Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
Martin Almquist <malmquist@stanford.edu>
parents:
950
diff
changeset
|
128 |
|
1049
0c504a21432d
Add getBoundaryQuadrature to all 1d diffOps
Martin Almquist <malmquist@stanford.edu>
parents:
1047
diff
changeset
|
129 % Returns square boundary quadrature matrix, of dimension |
|
0c504a21432d
Add getBoundaryQuadrature to all 1d diffOps
Martin Almquist <malmquist@stanford.edu>
parents:
1047
diff
changeset
|
130 % corresponding to the number of boundary points |
|
0c504a21432d
Add getBoundaryQuadrature to all 1d diffOps
Martin Almquist <malmquist@stanford.edu>
parents:
1047
diff
changeset
|
131 % |
|
0c504a21432d
Add getBoundaryQuadrature to all 1d diffOps
Martin Almquist <malmquist@stanford.edu>
parents:
1047
diff
changeset
|
132 % boundary -- string |
|
0c504a21432d
Add getBoundaryQuadrature to all 1d diffOps
Martin Almquist <malmquist@stanford.edu>
parents:
1047
diff
changeset
|
133 % Note: for 1d diffOps, the boundary quadrature is the scalar 1. |
|
0c504a21432d
Add getBoundaryQuadrature to all 1d diffOps
Martin Almquist <malmquist@stanford.edu>
parents:
1047
diff
changeset
|
134 function H_b = getBoundaryQuadrature(obj, boundary) |
|
0c504a21432d
Add getBoundaryQuadrature to all 1d diffOps
Martin Almquist <malmquist@stanford.edu>
parents:
1047
diff
changeset
|
135 assertIsMember(boundary, {'l', 'r'}) |
|
0c504a21432d
Add getBoundaryQuadrature to all 1d diffOps
Martin Almquist <malmquist@stanford.edu>
parents:
1047
diff
changeset
|
136 |
|
0c504a21432d
Add getBoundaryQuadrature to all 1d diffOps
Martin Almquist <malmquist@stanford.edu>
parents:
1047
diff
changeset
|
137 H_b = 1; |
|
0c504a21432d
Add getBoundaryQuadrature to all 1d diffOps
Martin Almquist <malmquist@stanford.edu>
parents:
1047
diff
changeset
|
138 end |
|
0c504a21432d
Add getBoundaryQuadrature to all 1d diffOps
Martin Almquist <malmquist@stanford.edu>
parents:
1047
diff
changeset
|
139 |
|
998
2b1b944deae1
Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
Martin Almquist <malmquist@stanford.edu>
parents:
950
diff
changeset
|
140 % Returns the boundary sign. The right boundary is considered the positive boundary |
|
2b1b944deae1
Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
Martin Almquist <malmquist@stanford.edu>
parents:
950
diff
changeset
|
141 % boundary -- string |
|
2b1b944deae1
Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
Martin Almquist <malmquist@stanford.edu>
parents:
950
diff
changeset
|
142 function s = getBoundarySign(obj, boundary) |
|
1042
8d73fcdb07a5
Add asserts to boundary identifier inputs
Jonatan Werpers <jonatan@werpers.com>
parents:
998
diff
changeset
|
143 assertIsMember(boundary, {'l', 'r'}) |
|
8d73fcdb07a5
Add asserts to boundary identifier inputs
Jonatan Werpers <jonatan@werpers.com>
parents:
998
diff
changeset
|
144 |
| 0 | 145 switch boundary |
|
998
2b1b944deae1
Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
Martin Almquist <malmquist@stanford.edu>
parents:
950
diff
changeset
|
146 case {'r'} |
|
2b1b944deae1
Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
Martin Almquist <malmquist@stanford.edu>
parents:
950
diff
changeset
|
147 s = 1; |
|
2b1b944deae1
Add getBoundaryOperator to all 1d schemes. Did not add getBoundaryQuadrature because it doesnt make sense in 1d (?)
Martin Almquist <malmquist@stanford.edu>
parents:
950
diff
changeset
|
148 case {'l'} |
| 0 | 149 s = -1; |
| 150 end | |
| 151 end | |
| 152 | |
| 153 function N = size(obj) | |
| 898 | 154 N = obj.grid.size(); |
| 0 | 155 end |
| 156 | |
| 157 end | |
|
1043
c12b84fe9b00
Remove static method `interface_coupling` that shouldn't have existed in the first place
Jonatan Werpers <jonatan@werpers.com>
parents:
950
diff
changeset
|
158 end |