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annotate inst/femfenics_examples.m @ 204:0faaf956bd3a

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Fix the HyperElasticity example
author gedeone-octave <marcovass89@hotmail.it>
date Thu, 30 Jan 2014 08:55:40 +0100
parents 3ae8a7398f43
children
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gedeone-octave <marcovass89@hotmail.it>
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1 ## Copyright (C) 2013 Marco Vassallo <gedeone-octave@users.sourceforge.net>
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2 ##
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3 ## This program is free software; you can redistribute it and/or modify it under
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4 ## the terms of the GNU General Public License as published by the Free Software
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5 ## Foundation; either version 3 of the License, or (at your option) any later
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6 ## version.
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7 ##
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8 ## This program is distributed in the hope that it will be useful, but WITHOUT
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9 ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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10 ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
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11 ## details.
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12 ##
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13 ## You should have received a copy of the GNU General Public License along with
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14 ## this program; if not, see <http://www.gnu.org/licenses/>.
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15
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16 %# -*- texinfo -*-
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17 %# @deftypefn {Function File} {[@var{}] =} femfenics_examples (@var{})
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18 %# Open the PDE examples menu and allow the user to select a demo that will be evaluated.
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19 %# @end deftypefn
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20
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21 function [] = femfenics_examples ()
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22
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23 vode = 1; while (vode > 0)
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24 clc;
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25 fprintf (1, ...
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26 ['FEM-FENICS examples menu:\n', ...
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27 '==================\n', ...
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28 '\n', ...
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29 ' (1) Solve the Poisson equation\n', ...
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30 ' (2) Solve the Poisson equation with a Mixed formulation\n', ...
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31 ' (3) Solve the Elasticity problem for an HyperElastic material\n', ...
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32 ' (4) Solve the Navier-Stokes equation with Chorin-Teman algorithm\n', ...
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33 ' (5) Solve the Biharmonic equation\n', ...
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34 '\n', ...
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35 ' Note: There are further FEM-FeNICS examples available with the pkg\n', ...
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36 ' testsuite functions.\n', ...
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37 '\n', ...
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38 ' If you have another interesting example that you would like\n', ...
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39 ' to share then please modify this file, create a patch and push\n', ...
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40 ' your patch with your added example to the Fem-Fenics repository.\n', ...
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41 '\n' ]);
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42 vode = input ('Please choose a number from above or press <Enter> to return: ');
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43 clc; if (vode > 0 && vode < 6)
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44 %# We can't use the function 'demo' directly here because it does
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45 %# not allow to run other functions within a demo.
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46 vexa = example (mfilename (), vode);
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47 disp (vexa);
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48 eval (vexa);
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49 input ('Press <Enter> to continue: ');
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50 end %# if (vode > 0)
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51 end %# while (vode > 0)
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52
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53 %!demo
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54 %! # In this example the Poisson equation is solved using P1 element
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55 %! # on a uniform squared mesh.
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56 %! # Read about the Poisson equation at
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57 %! # http://en.wikipedia.org/wiki/Poisson%27s_equation.
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58 %!
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59 %! n = length (mfilename ("fullpath")) - length (mfilename());
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60 %! path = strtrunc(mfilename ("fullpath"), n);
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61 %! private = fullfile (path, "example/Poisson/Poisson.ufl");
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62 %! [status, msg, msgid] = copyfile (private, pwd, 'f');
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63 %! if (status != 1)
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64 %! error ("couldn't copy file: %s", msg);
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65 %! endif
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66 %!
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67 %! pkg load fem-fenics msh
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68 %! import_ufl_Problem ('Poisson')
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69 %!
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70 %! # Create mesh and define function space
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71 %! x = y = linspace (0, 1, 33);
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72 %! mesh = Mesh(msh2m_structured_mesh (x, y, 1, 1:4));
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73 %!
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74 %! V = FunctionSpace('Poisson', mesh);
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75 %!
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76 %! # Define boundary condition
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77 %! bc = DirichletBC(V, @(x, y) 0.0, [2;4]);
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78 %!
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79 %! f = Expression ('f', @(x,y) 10*exp(-((x - 0.5)^2 + (y - 0.5)^2) / 0.02));
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80 %! g = Expression ('g', @(x,y) sin (5.0 * x));
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81 %!
165
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82 %! a = BilinearForm ('Poisson', V, V);
162
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83 %! L = LinearForm ('Poisson', V, f, g);
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84 %!
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85 %! # Compute solution
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86 %! [A, b] = assemble_system (a, L, bc);
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87 %! sol = A \ b;
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88 %! u = Function ('u', V, sol);
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89 %!
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90 %! # Save solution in VTK format
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91 %! save (u, 'poisson')
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92 %!
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93 %! # Plot solution
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94 %! plot (u);
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95
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96 %!demo
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97 %! # In this example the Poisson equation is solved using a Mixed Approach.
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98 %! # We use the stable FE space obtained using Brezzi-Douglas-Marini polynomial
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99 %! # of order 1 and Dicontinuos element of order 0.
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100 %! # Read about the Poisson equation at
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101 %! # http://en.wikipedia.org/wiki/Poisson%27s_equation.
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102 %!
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103 %! n = length (mfilename ("fullpath")) - length (mfilename());
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104 %! path = strtrunc(mfilename ("fullpath"), n);
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105 %! private = fullfile (path, "example/Mixed-Poisson/MixedPoisson.ufl");
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106 %! [status, msg, msgid] = copyfile (private, pwd, 'f');
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107 %! if (status != 1)
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108 %! error ("couldn't copy file: %s", msg);
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109 %! endif
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110 %!
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111 %! pkg load fem-fenics msh
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112 %! import_ufl_Problem ('MixedPoisson')
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113 %!
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114 %! # Create mesh
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115 %! x = y = linspace (0, 1, 33);
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116 %! mesh = Mesh(msh2m_structured_mesh (x, y, 1, 1:4));
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117 %!
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118 %! V = FunctionSpace('MixedPoisson', mesh);
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119 %!
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120 %! f = Expression ('f', @(x,y) 10*exp(-((x - 0.5)^2 + (y - 0.5)^2) / 0.02));
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121 %!
165
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122 %! a = BilinearForm ('MixedPoisson', V, V);
162
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123 %! L = LinearForm ('MixedPoisson', V, f);
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124 %!
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125 %! # Define essential boundary
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
126 %! bc1 = DirichletBC (SubSpace (V, 1), @(x,y) [0; -sin(5.0*x)], 1);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
127 %! bc2 = DirichletBC (SubSpace (V, 1), @(x,y) [0; sin(5.0*x)], 3);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
128 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
129 %! # Compute solution
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
130 %! [A, b] = assemble_system (a, L, bc1, bc2);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
131 %! sol = A \ b;
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
132 %! func = Function ('func', V, sol);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
133 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
134 %! sigma = Function ('sigma', func, 1);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
135 %! u = Function ('u', func, 2);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
136 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
137 %! # Plot solution
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
138 %! plot (sigma);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
139 %! plot (u);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
140
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
141 %!demo
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
142 %! # In this example we solve the equation for an Hyperelastic material
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
143 %! # minimizing the potential energy of the material.
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
144 %! # Read about the Hyperelastic materials at
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
145 %! # http://en.wikipedia.org/wiki/Hyperelastic_material
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
146 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
147 %! n = length (mfilename ("fullpath")) - length (mfilename());
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
148 %! path = strtrunc(mfilename ("fullpath"), n);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
149 %! private = fullfile (path, "example/Elasticity/HyperElasticity.ufl");
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
150 %! [status, msg, msgid] = copyfile (private, pwd, 'f');
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
151 %! if (status != 1)
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
152 %! error ("couldn't copy file: %s", msg);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
153 %! endif
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
154 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
155 %! pkg load fem-fenics msh
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
156 %! problem = 'HyperElasticity';
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
157 %! import_ufl_Problem (problem);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
158 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
159 %! Rotation = @(x,y,z) ...
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
160 %! [0; ...
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
161 %! 0.5*(0.5 + (y - 0.5)*cos(pi/3) - (z-0.5)*sin(pi/3) - y);...
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
162 %! 0.5*(0.5 + (y - 0.5)*sin(pi/3) + (z-0.5)*cos(pi/3) - z)];
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
163 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
164 %! #Create mesh and define function space
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
165 %! x = y = z = linspace (0, 1, 17);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
166 %! mshd = Mesh (msh3m_structured_mesh (x, y, z, 1, 1:6));
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
167 %! V = FunctionSpace (problem, mshd);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
168 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
169 %! # Create Dirichlet boundary conditions
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
170 %! bcl = DirichletBC (V, @(x,y,z) [0; 0; 0], 1);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
171 %! bcr = DirichletBC (V, Rotation, 2);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
172 %! bcs = {bcl, bcr};
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
173 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
174 %! # Define source and boundary traction functions
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
175 %! B = Constant ('B', [0.0; -0.5; 0.0]);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
176 %! T = Constant ('T', [0.1; 0.0; 0.0]);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
177 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
178 %! # Set material parameters
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
179 %! E = 10.0;
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
180 %! nu = 0.3;
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
181 %! mu = Constant ('mu', E./(2*(1+nu)));
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
182 %! lmbda = Constant ('lmbda', E*nu./((1+nu)*(1-2*nu)));
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
183 %! u = Expression ('u', @(x,y,z) [0; 0; 0]);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
184 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
185 %! # Create (linear) form defining (nonlinear) variational problem
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
186 %! L = ResidualForm (problem, V, mu, lmbda, B, T, u);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
187 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
188 %! # Solve nonlinear variational problem F(u; v) = 0
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
189 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
190 %! # Create function for the resolution of the NL problem
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
191 %! function [y, jac] = f (problem, xx, V, bc1, bc2, B, T, mu, lmbda)
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
192 %! u = Function ('u', V, xx);
204
0faaf956bd3a Fix the HyperElasticity example
gedeone-octave <marcovass89@hotmail.it>
parents: 165
diff changeset
193 %! a = JacobianForm (problem, V, V, mu, lmbda, u);
162
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
194 %! L = ResidualForm (problem, V, mu, lmbda, B, T, u);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
195 %! if (nargout == 1)
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
196 %! [y, xx] = assemble (L, xx, bc1, bc2);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
197 %! elseif (nargout == 2)
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
198 %! [jac, y, xx] = assemble_system (a, L, xx, bc1, bc2);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
199 %! endif
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
200 %! endfunction
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
201 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
202 %! u0 = assemble (L, bcs{:});
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
203 %! fs = @(xx) f (problem, xx, V, bcl, bcr, B, T, mu, lmbda);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
204 %! [x, fval, info] = fsolve (fs, u0, optimset ("jacobian", "on"));
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
205 %! func = Function ('u', V, x);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
206 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
207 %! # Save solution in VTK format
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
208 %! save (func, 'displacement');
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
209 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
210 %! # Plot solution
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
211 %! plot (func);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
212
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
213 %!demo
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
214 %! # In this example we solve the Navier-Stokes equation in a L-shape domain.
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
215 %! # We impose a sinusoidal pressure at the inflow and a constant pressure at
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
216 %! # the output. On the other sides, no-slip BC are applied.
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
217 %! # We solve the problem with the Chorin-Temam algorithm.
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
218 %! # The pressure is discretized with P1 element while the velocity with P2.
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
219 %! # Read about the NS equation at
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
220 %! # http://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
221 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
222 %! n = length (mfilename ("fullpath")) - length (mfilename());
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
223 %! path = strtrunc(mfilename ("fullpath"), n);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
224 %! private = fullfile (path, "example/NavierStokes/*.ufl");
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
225 %! [status, msg, msgid] = copyfile (private, pwd, 'f');
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
226 %! if (status != 1)
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
227 %! error ("couldn't copy file: %s", msg);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
228 %! endif
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
229 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
230 %! pkg load fem-fenics msh
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
231 %! import_ufl_Problem ("TentativeVelocity");
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
232 %! import_ufl_Problem ("VelocityUpdate");
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
233 %! import_ufl_Problem ("PressureUpdate");
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
234 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
235 %! # We use the msh pkg to generate the L-shape domain
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
236 %! name = [tmpnam ".geo"];
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
237 %! fid = fopen (name, "w");
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
238 %! fputs (fid,"Point (1) = {0, 0, 0, 0.1};\n");
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
239 %! fputs (fid,"Point (2) = {1, 0, 0, 0.1};\n");
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
240 %! fputs (fid,"Point (3) = {1, 0.5, 0, 0.1};\n");
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
241 %! fputs (fid,"Point (4) = {0.5, 0.5, 0, 0.1};\n");
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
242 %! fputs (fid,"Point (5) = {0.5, 1, 0, 0.1};\n");
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
243 %! fputs (fid,"Point (6) = {0, 1, 0,0.1};\n");
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
244 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
245 %! fputs (fid,"Line (1) = {5, 6};\n");
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
246 %! fputs (fid,"Line (2) = {2, 3};\n");
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
247 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
248 %! fputs (fid,"Line(3) = {6,1,2};\n");
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
249 %! fputs (fid,"Line(4) = {5,4,3};\n");
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
250 %! fputs (fid,"Line Loop(7) = {3,2,-4,1};\n");
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
251 %! fputs (fid,"Plane Surface(8) = {7};\n");
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
252 %! fclose (fid);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
253 %! msho = msh2m_gmsh (canonicalize_file_name (name)(1:end-4),"scale", 1,"clscale", .4);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
254 %! unlink (canonicalize_file_name (name));
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
255 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
256 %! mesh = Mesh (msho);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
257 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
258 %! # Define function spaces (P2-P1). From ufl file
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
259 %! V = FunctionSpace ('VelocityUpdate', mesh);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
260 %! Q = FunctionSpace ('PressureUpdate', mesh);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
261 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
262 %! # Set parameter values
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
263 %! dt = 0.01;
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gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
264 %! T = 3.;
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
265 %!
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gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
266 %! # Define boundary conditions
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
267 %! noslip = DirichletBC (V, @(x,y) [0; 0], [3, 4]);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
268 %! outflow = DirichletBC (Q, @(x,y) 0, 2);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
269 %!
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gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
270 %! # Create functions
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
271 %! u0 = Expression ('u0', @(x,y) [0; 0]);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
272 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
273 %! # Define coefficients
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gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
274 %! k = Constant ('k', dt);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
275 %! f = Constant ('f', [0; 0]);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
276 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
277 %! # Tentative velocity step.
165
3ae8a7398f43 Update the examples for the tutorial.
gedeone-octave <marcovass89@hotmail.it>
parents: 162
diff changeset
278 %! a1 = BilinearForm ('TentativeVelocity', V, V, k);
162
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
279 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
280 %! # Pressure update.
165
3ae8a7398f43 Update the examples for the tutorial.
gedeone-octave <marcovass89@hotmail.it>
parents: 162
diff changeset
281 %! a2 = BilinearForm ('PressureUpdate', Q, Q);
162
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
282 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
283 %! # Velocity update
165
3ae8a7398f43 Update the examples for the tutorial.
gedeone-octave <marcovass89@hotmail.it>
parents: 162
diff changeset
284 %! a3 = BilinearForm ('VelocityUpdate', V, V);
162
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
285 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
286 %! # Assemble matrices
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
287 %! A1 = assemble (a1, noslip);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
288 %! A3 = assemble (a3, noslip);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
289 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
290 %! # Time-stepping
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
291 %! t = dt; i = 0;
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
292 %! while t < T
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
293 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
294 %! # Update pressure boundary condition
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
295 %! inflow = DirichletBC (Q, @(x,y) sin(3.0*t), 1);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
296 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
297 %! # Compute tentative velocity step
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
298 %! L1 = LinearForm ('TentativeVelocity', V, k, u0, f);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
299 %! b1 = assemble (L1, noslip);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
300 %! utmp = A1 \ b1;
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
301 %! u1 = Function ('u1', V, utmp);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
302 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
303 %! # Pressure correction
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
304 %! L2 = LinearForm ('PressureUpdate', Q, u1, k);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
305 %! [A2, b2] = assemble_system (a2, L2, inflow, outflow);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
306 %! ptmp = A2 \ b2;
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
307 %! p1 = Function ('p1', Q, ptmp);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
308 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
309 %! # Velocity correction
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
310 %! L3 = LinearForm ('VelocityUpdate', V, k, u1, p1);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
311 %! b3 = assemble (L3, noslip);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
312 %! ut = A3 \ b3;
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
313 %! u1 = Function ('u0', V, ut);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
314 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
315 %! # Plot solution
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
316 %! plot (p1);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
317 %! plot (u1);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
318 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
319 %! # Save to file
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
320 %! save (p1, sprintf ("p_%3.3d", ++i));
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
321 %! delete (sprintf ("p_%3.3d.pvd", i));
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
322 %! save (u1, sprintf ("u_%3.3d", i));
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
323 %! delete (sprintf ("u_%3.3d.pvd", i));
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
324 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
325 %! # Move to next time step
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
326 %! u0 = u1;
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
327 %! t += dt
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
328 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
329 %! end
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
330
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
331 %!demo
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
332 %! # In this example the Biharmonic equation is solved using P2 element
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
333 %! # on a uniform squared mesh.
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
334 %! # Read more about the Biharmonic equation at
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
335 %! # http://en.wikipedia.org/wiki/Biharmonic
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
336 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
337 %! n = length (mfilename ("fullpath")) - length (mfilename());
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
338 %! path = strtrunc(mfilename ("fullpath"), n);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
339 %! private = fullfile (path, "example/Biharmonic/Biharmonic.ufl");
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
340 %! [status, msg, msgid] = copyfile (private, pwd, 'f');
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
341 %! if (status != 1)
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
342 %! error ("couldn't copy file: %s", msg);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
343 %! endif
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
344 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
345 %! pkg load fem-fenics msh
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
346 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
347 %! problem = 'Biharmonic';
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
348 %! import_ufl_Problem (problem);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
349 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
350 %! # Create mesh and define function space
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
351 %! x = y = linspace (0, 1, 33);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
352 %! mesh = Mesh(msh2m_structured_mesh (x, y, 1, 1:4));
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
353 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
354 %! V = FunctionSpace(problem, mesh);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
355 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
356 %! bc = DirichletBC (V, @(x,y) 0, 1:4);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
357 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
358 %! f = Expression ('f', @(x,y) 4.0*pi^4.*sin(pi.*x).*sin(pi.*y));
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
359 %! g = Expression ('alpha', @(x,y) 8);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
360 %!
165
3ae8a7398f43 Update the examples for the tutorial.
gedeone-octave <marcovass89@hotmail.it>
parents: 162
diff changeset
361 %! a = BilinearForm (problem, V, V, g);
162
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
362 %! L = LinearForm (problem, V, f);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
363 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
364 %! [A, b] = assemble_system (a, L, bc);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
365 %! u = A \ b;
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
366 %!
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
367 %! func = Function ('u', V, u);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
368 %! plot (func);
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
369
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
370 %# Local Variables: ***
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
371 %# mode: octave ***
344e9bc30b03 New file for the ecxamples associated with the pkg.
gedeone-octave <marcovass89@hotmail.it>
parents:
diff changeset
372 %# End: ***