A New Twist on Maxwell
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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.
Since the advent of com-
puter analysis, engineers
and scientists have
struggled to get accurate numerical solutions to Maxwell's equations.
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.
According to Adams, the computational difficulty has been most
acute for people working in electromagnetic radiation and scattering
and scalar wave theory. "Conventional simulations of Maxwell's
equations are unstable as the frequency gets low. A number of
people have published incorrect results as a consequence,"
"There is nothing wrong with Maxwell's equations - until
you try to solve them on the computer," he said. "Until
now, the implementations have been ill posed."
Maxwell's equations simply describe how fields behave, he said.
"There is more than one way to say the same thing, however.
What people have been doing with computational methods is to
write them in the form most easily adapted to being implemented
on the computer. These formulations have been ill posed."
When these ill-posed formulations become unstable, people have
"tweaked" the simulations to approximate reasonable
answers. "One problem with tweaking is that the code is
more inefficient," he explained. "But the biggest problem
is that you do not know when the tweaking will break down. You
cannot trust your answers."
The ill-posedness of the original formulation is a problem at
all frequencies, he said, but is a particular problem in low
frequencies. "We've developed a well-posed formulation for
all frequencies. People have developed different formulations
for different frequencies, but ours works in all ranges,"
When discussing low frequency, Adams is referring to the size
of an object relative to the electromagnetic wavelength. "A
low frequency is one in which a radius is a small fraction (such
as one-tenth) of a wavelength. With a sphere of radius 1 meter,
low frequency would be around 30 MHz. With a sphere of radius
100 meters, low frequency would be 300 kHz."
His results will be useful to anybody doing electromagnetic simulations
and similar equations, such as those governing acoustics. Adams'
work is generating significant interest in the field, he said.
Hughes Electronics Corp. is incorporating the new formulation
into their general code, as is the Lawrence Livermore National
Laboratory. A group at the University of Kentucky is interested
in using it to develop simulation codes for the microwave frequency
in their work simulating printed circuits.
Adams developed the new formulation as a Bradley Fellow working
on his dissertation in the department's ElectroMagnetic
Interactions Laboratory (EMIL). He
had earned his master's degree working on incoherent short pulse
scattering from penetrable geophysical terrain. "I decided
that my master's work was more phenomenological modeling, and
I wanted to do some detailed basic work with Maxwell's equations.
The best way to do that was with numerical methods, actually
developing algorithms to implement equations on a computer.
"The Bradley Fellowship allowed me to do that. It is hard
to find research funding at the Graduate Research Assistant level
for theoretical work like that."
Adams' inclination toward the theoretical is long standing. He
entered college at Michigan Tech to study applied physics. However,
in college he decided that he would be more employable as an
engineer. "I co-opped at a nuclear power plant and decided
I didn't want to be that applied." So he decided to go to
graduate school, and came to Virginia Tech to study communications.
At Tech, he grew interested in the theoretical aspects of electromagnetics,
and joined EMIL.
After finishing his dissertation, Adams decided to engage in
post doctoral work to follow up on the applications of his Ph.D.
research. "We had many ideas that were pretty new and needed
an infrastructure to develop and implement them," he said.
The department offered him a Bradley Post-Doctoral Fellowship
in order to further develop his fundamental work to the point
where industrial funding was possible. "The initial fundamental
ideas were not directly applicable to end users," he said.
The post-doctoral fellowship allowed me to develop the work to
the point where many people can apply it. Without the Fellowship,
this work would not have been developed at Tech."