Multi-Model Multi-Domain Computational Methods: An Example Helmholtz Problem

Below are some solutions for a simple two-dimensional model Helmholtz problem in an eccentric annulus. This example employs a single point source located at (-0.5,0.0), as represented by Neumann boundary conditions on the inner circle of radius 1.0. The artificial farfield boundary is a circle centered at the origin with a radius of 2.0, where a nonreflecting boundary condition that eliminates spurious reflections is imposed via a Dirichlet-to-Neumann map.

This model has proven useful in investigations of both farfield and interior subdomain boundary conditions, as discussed further in these references.

Real (left) and imaginary (right) components of the solution, wave number k=4.

Real (left) and imaginary (right) components of the solution, wave number k=10.