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Spring 2001



New Method Gives Correct Simulation Results of Maxwell's Equations at All Frequencies

Robert Adams (Ph.D., '98) is the first person to develop an elegant method of simulating Maxwell's equations with consistently stable and correct results in all frequencies.

Consistently stable and accurate computer simulations of Maxwell's equations at all frequencies are now possible with a new method developed by Robert Adams (Ph.D., '98), a research assistant professor with the department's ElectroMagnetic Interactions Laboratory (EMIL).

Since the advent of computer analysis, engineers and scientists have struggled to get accurate numerical solutions to Maxwell's equations. These computational difficulties have limited the practical usefulness of numerical simulation methods for electromagnetic phenomena, Adams said.

"Conventional simulations of Maxwell's equations are unstable as the frequency gets low. A number of people have published incorrect results as a consequence," he said. "Surprisingly, these low-frequency instabilities also prevent the accurate and efficient simulation of high-frequency field behaviors."
"There is nothing wrong with traditional formulations of Maxwell's equations - until we simulate them on finite-precision machines," he said.

According to Adams, researchers have been performing numerical simulations using the classical representations of Maxwell's equations found in most textbooks. "In many cases, these formulations are ill-posed," he said. The traditional formulations can be patched-up to extend their ranges of validity, "but the biggest problem is that we usually don't know when this ad hoc approach will break. It becomes difficult to have confidence in the results of a simulation."

The ill-posedness of the original formulations is a problem at all frequencies, he said, but it becomes particularly acute at low frequencies. "We've developed a single formulation that is uniformly well-posed at all frequencies. People have previously developed different approaches for different frequencies, but ours works gracefully in all ranges," he said.

When discussing low frequency, Adams is referring to the size of an object relative to the electromagnetic wavelength. His results will be useful to anybody simulating scalar and vector wave phenomena.

The Bradley Department of Electrical and Computer Engineering
Virginia Tech

Last Updated, July 25, 2001
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