Time-Domain Algorithms for Computational Electromagnetics (AlgoCEM)

Waves Impinging on Planar Boundary (click for more info)

Nonreflecting Boundary Kernels (click for more info)

Computational Electromagnetics

Applications that require modeling of electromagnetic (and acoustic) wave propagation are extremely broad, ranging over

Device design

Antennas and waveguides

Microcircuits and transducers

Low-observable aircraft

Nondestructive testing

Turbines

Jet engines

Railroad wheels (acoustics)

Imaging

Geophysics

Medicine

Target identification

At NIST, applications include the modeling of antennas (including those on integrated circuits), waveguides (microwave and photonic), transducers, and in nondestructive testing.

Time-Domain Methods

Radiation and scattering of acoustic and electromagnetic waves are increasingly modeled using time-domain computational methods, due to their flexibility in handling

Wide-Band signals,
Material inhomogeneities, and
Nonlinearities.

For many applications, the accuracy of the computed models is centrally important. Nevertheless, existing methods typically allow for only limited control over accuracy and cannot achieve high accuracy for reasonable computational cost.

Project Goals

This project, a collaborative effort directed by B. Alpert (NIST), L. Greengard (New York University), and T. Hagstrom (University of New Mexico), and supported in part by the Defense Advanced Research Projects Agency (DARPA) Applied and Computational Mathematics Program, has the goal of the development of algorithms and codes for high-accuracy time-domain computations, addressing key weaknesses of existing methods, specifically

Accurate nonreflecting boundary conditions (that reduce an infinite physical domain to a finite computational domain),
Suitable geometric representations of scattering objects, and
High-order, stable spatial and temporal discretizations for realistic scatterer geometries.

Progress to Date

Fundamental progress in numerical algorithms for wave propagation has been achieved by the project, in two of these areas:

Efficient computation of the exact nonreflecting boundary conditions, reported in
Bradley Alpert, Leslie Greengard, and Thomas Hagstrom, Rapid Evaluation of Nonreflecting Boundary Kernels for Time-Domain Wave Propagation, SIAM Journal on Numerical Analysis 37, 1138-1164 (2000),
Bradley Alpert, Leslie Greengard, and Thomas Hagstrom, Nonreflecting Boundary Conditions for the Time-Dependent Wave Equation, Journal of Computational Physics 180, 270-296 (2002),

High-order convergent discretization techniques, reported in
B. Alpert, L. Greengard, T. Hagstrom, An Integral Evolution Formula for the Wave Equation, Journal of Computational Physics 162, 1-8 (2000), and

Representation of Waves in Unbounded Domains, reported in
Bradley K. Alpert and Yu Chen, A Representation of Acoustic Waves in Unbounded Domains, Communications in Pure and Applied Mathematics LVIII (10), 1358-1374 (2005).

A project of the Mathematical and Computational Sciences Division of NIST.

Bradley K Alpert

Last modified: Thur Jan 26 8:54:20 MDT 2005