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Bim package: Difference between revisions
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<math> u(x, y) = u_d(x, y)\qquad \mbox{ on } \Gamma_D </math> | <math> u(x, y) = u_d(x, y)\qquad \mbox{ on } \Gamma_D </math> | ||
<math> -( \varepsilon\ \nabla u(x, y) - \nabla \varphi(x,y)\ u(x, y) ) \cdot \mathbf{n} \qquad \mbox{ on } \Gamma_N</math> | <math> -( \varepsilon\ \nabla u(x, y) - \nabla \varphi(x,y)\ u(x, y) ) \cdot \mathbf{n} = j_N(x, y)\qquad \mbox{ on } \Gamma_N</math> | ||
<b> Create the mesh and precompute the mesh properties </b> | <b> Create the mesh and precompute the mesh properties </b> | ||
To define the geometry of the domain we can use [http://gmsh.geuz.org gmsh]. | |||
the following gmsh input | |||
<pre> | |||
Point (1) = {0, 0, 0, 0.1}; | |||
Point (2) = {1, 1, 0, 0.1}; | |||
Point (3) = {1, 0.9, 0, 0.1}; | |||
Point (4) = {0, 0.1, 0, 0.1}; | |||
Point (5) = {0.3,0.1,-0,0.1}; | |||
Point (6) = {0.4,0.4,-0,0.1}; | |||
Point (7) = {0.5,0.6,0,0.1}; | |||
Point (8) = {0.6,0.9,0,0.1}; | |||
Point (9) = {0.8,0.8,0,0.1}; | |||
Point (10) = {0.2,0.2,-0,0.1}; | |||
Point (11) = {0.3,0.5,0,0.1}; | |||
Point (12) = {0.4,0.7,0,0.1}; | |||
Point (13) = {0.5,1,0,0.1}; | |||
Point (14) = {0.8,0.9,0,0.1}; | |||
Line (1) = {3, 2}; | |||
Line (2) = {4, 1}; | |||
CatmullRom(3) = {1,5,6,7,8,9,3}; | |||
CatmullRom(4) = {4,10,11,12,13,14,2}; | |||
Line Loop(15) = {3,1,-4,2}; | |||
Plane Surface(16) = {15}; | |||
</pre> | |||
will produce the geometry below | |||
[[File:fiume.png]] | [[File:fiume.png]] | ||
we need to load the mesh into Octave and precompute mesh properties | |||
check out the tutorial for the [[msh_package|msh package]] for info | |||
on the mesh structure | |||
<pre> | <pre> | ||
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</pre> | </pre> | ||
to see the mesh you can use functions from the [fpl] | to see the mesh you can use functions from the [[fpl_package|fpl package]] | ||
<pre> | <pre> | ||
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<b> Construct an initial guess</b> | <b> Construct an initial guess</b> | ||
<b> Set the coefficients for the problem:</b> | |||
Get the node coordinates from the mesh structure | Get the node coordinates from the mesh structure | ||
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</pre> | </pre> | ||
Get the number of elements and nodes in the mesh | Get the number of elements and nodes in the mesh | ||
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<pre> | <pre> | ||
epsilon = .1; | epsilon = .1; | ||
phi = xu+yu; | phi = xu + yu; | ||
</pre> | </pre> | ||
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<pre> | <pre> | ||
GammaD = bim2c_unknowns_on_side(mesh, [1 2]); ## DIRICHLET NODES LIST | |||
GammaN = bim2c_unknowns_on_side(mesh, [3 4]); ## NEUMANN NODES LIST | |||
Corners = setdiff(GammaD,GammaN); | |||
jn = zeros(length(GammaN),1); ## PRESCRIBED NEUMANN FLUXES | |||
ud = 3*xu; ## DIRICHLET DATUM | |||
Ilist = setdiff(1:length(uin),union(Dlist,Nlist)); ## INTERNAL NODES LIST | Ilist = setdiff(1:length(uin),union(Dlist,Nlist)); ## INTERNAL NODES LIST | ||
</pre> | </pre> | ||