Wavelets and the Numerical Solution of Heat Transfer Problems: A Discussion of Two Methods

Two methods for solving heat transfer problems using wavelets are reviewed and discussed, namely the so-called “Fictitious Boundary” and “Fictitious Domain/Penalty” methods. Evaluation of the two methods is performed by solving simple two-dimensional heat conduction problems using fixed scale expansion of the unknowns. A discussion on the implemention of the boundary conditions and the ease of solving the resulting system of equations is presented. For each problem the error is computed so that the accuracy of the solution can be evaluated. It is found that the Fictitious Domain/Penalty method shows better agreement with the exact solutions than the Fictitious Boundary method as it introduces less computational errors due the methodology used to implement the boundary conditions in the extended domain.