Bim package: Difference between revisions

Bim package (edit)

Revision as of 21:19, 19 July 2012

258 bytes added , 19 July 2012

no edit summary

Carlo

43

edits

@@ Line 6: / Line 6: @@
 We want to solve the equation
-<math>  -\mathrm{div}\ ( \varepsilon\ \nabla u(x, y) - \nabla \varphi(x,y)\ u(x, y) ) ) + u(x, y) = 1 </math>
+<math>  -\mathrm{div}\ ( \varepsilon\ \nabla u(x, y) - \nabla \varphi(x,y)\ u(x, y) ) ) + u(x, y) = 1 \qquad in \Omega</math>
+<math>  \varphi(x, y)\ =\ x + y </math>
+with mixed Dirichlet / Neumann boundary conditions
-<math>  \varphi(x, y)\ =\ x + y </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>
 <b> Create the mesh and precompute the mesh properties </b>
@@ Line 34: / Line 38: @@
 <b> Construct an initial guess</b>
-For a linear problem only the values at boundary nodes are actually relevant<br>
+We need this even if our problem is linear and stationary
+as we are going to use the values at boundary nodes to set
+Dirichelet boundary conditions.
+Get the node coordinates from the mesh structure
 <pre>
 xu     = mesh.p(1,:).';
 yu     = mesh.p(2,:).';
-nelems = columns(mesh.t);
+</pre>
-nnodes = columns(mesh.p);
+<pre>
 uin    = 3*xu;
 </pre>
@@ Line 46: / Line 56: @@
 <b> Set the coefficients for the problem:</b>
+Get the number of elements and nodes in the mesh
+<pre>
+nelems = columns(mesh.t);
+nnodes = columns(mesh.p);
+</pre>
 <pre>
 epsilon = .1;
-alfa    = ones(nelems,1);
+phi     = xu+yu;
-gamma   = ones(nnodes,1);
-eta     = epsilon*ones(nnodes,1);
-beta    = xu+yu;
-delta   = ones(nelems,1);
-zeta    = ones(nnodes,1);
-f       = ones(nelems,1);
-g       = ones(nnodes,1);
 </pre>
@@ Line 62: / Line 71: @@
 <pre>
-AdvDiff = bim2a_advection_diffusion(mesh,alfa,gamma,eta,beta);
+AdvDiff = bim2a_advection_diffusion(mesh, epsilon, 1, phi);
 Mass    = bim2a_reaction(mesh,delta,zeta);
 b       = bim2a_rhs(mesh,f,g);