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Nonreflecting Boundary Conditions for the Time-Dependent Wave Equation

Bradley K. Alpert, ACMD
Leslie F. Greengard, Courant Institute for Mathematical Sciences
Thomas M. Hagstrom, University of New Mexico

Numerical methods to solve the time-dependent wave equation, applicable to a variety of electromagnetic and acoustic problems, generally require some technique to truncate an infinite physical domain to a finite computational domain, yet preserve the outgoing radiation property (Sommerfeld radiation condition). The task of incorporating this well-known physical constraint into an effective computational procedure has been widely studied, but existing approaches do not achieve good accuracy. In many time-domain computational models, reflections from the computational boundary comprise the largest source of error in the model.

A variety of wave problems occurring at NIST are amenable to modeling using time-domain methods. These include determination of material dielectric constants using resonance cavities, calibration of electromagnetic probes, characterization of microwave and optical transmission lines, and characterization of material defects by acoustic emissions. For each of these problems, model inaccuracy is an important issue limiting the acceptance of numerical methods.

This project, currently at an early stage, has been formed around a recent mathematical observation that is expected to lead to effective numerical procedures to model nonreflecting boundaries to arbitrary accuracy. Assuming the observation leads to a workable algorithm, the project team plans to create software for the solution of a variety of electromagnetic problems.