Bim package: Difference between revisions

Bim package (edit)

Revision as of 21:51, 19 July 2012

678 bytes added , 19 July 2012

no edit summary

Carlo

43

edits

@@ Line 13: / Line 13: @@
 <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>
-The geometry of the domain was created using gmsh and is stored in the file <tt>fiume.geo</tt>
+To define the geometry of the domain we can use [http://gmsh.geuz.org gmsh].
-created with [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]]
+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>
@@ Line 27: / Line 59: @@
 </pre>
-to see the mesh you can use functions from the [fpl] package
+to see the mesh you can use functions from the [[fpl_package|fpl package]]
 <pre>
@@ Line 38: / Line 70: @@
 <b> Construct an initial guess</b>
-We need this even if our problem is linear and stationary
+<b> Set the coefficients for the problem:</b>
-as we are going to use the values at boundary nodes to set
-Dirichelet boundary conditions.
 Get the node coordinates from the mesh structure
@@ Line 49: / Line 79: @@
 </pre>
-<pre>
-uin    = 3*xu;
-</pre>
-<b> Set the coefficients for the problem:</b>
 Get the number of elements and nodes in the mesh
@@ Line 65: / Line 89: @@
 <pre>
 epsilon = .1;
-phi     = xu+yu;
+phi     = xu + yu;
 </pre>
@@ Line 82: / Line 106: @@
 <pre>
-Dlist = bim2c_unknowns_on_side(mesh, [8 18]); 	   ## DIRICHLET NODES LIST
+GammaD = bim2c_unknowns_on_side(mesh, [1 2]); 	   ## DIRICHLET NODES LIST
-Nlist = bim2c_unknowns_on_side(mesh, [23 24]); 	   ## NEUMANN NODES LIST
+GammaN = bim2c_unknowns_on_side(mesh, [3 4]); 	   ## NEUMANN NODES LIST
-Nlist = setdiff(Nlist,Dlist);
+Corners = setdiff(GammaD,GammaN);
-Fn    = zeros(length(Nlist),1);           	   ## PRESCRIBED NEUMANN FLUXES
+jn    = zeros(length(GammaN),1);           	   ## PRESCRIBED NEUMANN FLUXES
+ud    = 3*xu;                                      ## DIRICHLET DATUM
 Ilist = setdiff(1:length(uin),union(Dlist,Nlist)); ## INTERNAL NODES LIST
 </pre>