Nonreflecting Boundary Conditions Obtained from Equivalent Sources for Time-Dependent Scattering Problems

Citation

Hoch, David (2008) Nonreflecting Boundary Conditions Obtained from Equivalent Sources for Time-Dependent Scattering Problems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/5M0P-NR33. https://resolver.caltech.edu/CaltechETD:etd-05202008-111349

Abstract

In many engineering applications, scattering of acoustic or electromagnetic waves from a body of arbitrary shape is considered in an infinite medium. Solving the underlying partial differential equations with a standard numerical method such as finite elements or finite differences requires truncating the unbounded domain of definition into a finite computational region. As a consequence, an appropriate boundary condition must be prescribed at the artificial boundary. Many approaches have been proposed for this fundamental problem in the field of wave scattering. All of them fall into one of three main categories.

The first class of methods is based on mathematical approximations or physical heuristics. These boundary conditions are easy to implement and run in short computing times. However, these approaches give rise to spurious reflections at the artificial boundary, which travel back into the computational domain and corrupt the solution.

A second group consists of accurate and convergent methods. However, these formulations are usually harder to implement and often more expensive than the computation of the interior scheme itself.

Finally, there are methods which are accurate and fast. The drawback of these approaches lies in the fact that the outer boundary must be taken to be either a sphere, a plane, or a cylinder. For many applications of interest, this may require use of a computational domain much larger than actually needed, which leads to an expensive overall numerical scheme.

This work introduces a new methodology in order to compute the fields at the artificial boundary. Like the second class of methods described above, the proposed algorithm is accurate and numerically convergent, yet its computational cost is less than the underlying portion of the volumetric calculation. And, unlike the third category, this new approach allows us to choose the artificial boundary to be arbitrarily close to the scatterer. This method is based on a novel concept of "equivalent source' representations which allows a highly accurate and fast evaluation of the boundary condition.

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