Laplace solvers

• Dirichlet boundary value problem

Dirichlet boundary value problem

The dirichlet problem for the Laplace equation is given by

\[\begin{split}\Delta u &= 0 \quad \mbox{ in } \Omega \, , \\ u &= f \quad \mbox{ on } \Gamma \, .\end{split}\]

For solving the above problem, we represent \(u\) in \(\Omega\) using the combined field representation:

\[u = \alpha \mathcal{S}_{0}[\sigma] + \beta \mathcal{D}_{0}[\sigma] \,.\]

We have the following user callable routines:

• Dirichlet iterative solver

• Dirichlet post-processor

To see a demo of the use of these interfaces see examples/laplace/lap_dir_iter_example.f. This script can be run using make -f lap_dir_iter_example.make in the examples/laplace folder.