A quick look at solving PDEs via Multi-dimensional WDFs

Basic idea:

Replace a system of PDEs by a set of Kirchoff Loop Equations, each of which contains multidimensional (distributed) circuit elements.

Benefits:

• Associates a passive set of equations with a passive electrical circuit $\Rightarrow$ good stability properties.

• Algorithm will be explicit, parallelizable

• Extensions possible to non constant-coefficient, nonlinear problems, still retaining stability properties.

Drawbacks:

• Only works for PDEs derived from conservation relations (a small, but important class)

• Convergence may be slow.

Reference: Stefan Bilbao's thesis