Heat Transfer Demo 4

Heat Transfer Demo 4: An eigenvalue problem

Here is a simple example to calculate eigenvalues and eigenvectors of an elliptic problem. We compute some eigenvalues of the Laplace operator using the Bathe subspace iteration method..

As usual, we construct an instance of class IPF to manage project data. We extract useful information from this instance: namely, the mesh file name and the number of eigenvalues to extract. Next, we construct the mesh and remove essential boundary conditions from the unknowns: This is essential for solving the eigenvalue problem.

IPF data(argv[1]); int nb = data.getInteger("nb"); Mesh ms(data.getMeshFile()); ms.removeImposedDOF();

After outputting some information about the code, we declare an instance of class Mesh and remove imposed boundary conditions: In fact, in view of using an iterative procedure to solve the linear system. Penalty techniques are not efficient in this case.

Laplace2DT3 eq(ms); eq.solveEigenProblem(nb);

In order to read various prescriptions (boundary conditions, heat sources, fluxes), we use the class Prescription. The name of the file containing these prescriptions is given in data.getDataFile()

cout << "Nb. of iterations: " << eq.getEigenSolver().getNbIter() << endl; Vect v; for (int i=1; i<=nb; i++) { cout << "Eigenvalue #" << i << ": " << eq.getEigenValue(i) << endl; eq.getEigenVector(i,v); IOField ff(data.getMeshFile(),data.getPlotFile(i),ms,OUT); ff.put(NodeVect(ms,v)); }

An example

Let us run this program with the data presented in the following project file:

<?xml version="1.0" encoding="ISO-8859-1" ?> <OFELI_File> <info> <title></title> <date></date> <author></author> </info> <Project name="eigen"> <mesh_file value="square-20.m" /> <parameter label="nb" value="2" /> <plot_file value="test.ev1" /> <plot_file value="test.ev2" /> </Project> </OFELI_File>

In summary, this file looks mainly like the one in the previous example.