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Modeling Sound Waves and Electric Fields to Improve Hearing Aids and Aircraft Antennas

Leszek Demkowicz
Texas Institute for Computational and Applied Mathematics (TICAM), University of Texas

Waldek Rachowicz, Andrzej Bajer, Timothy Walsh, Satish Chavva, TICAM
Richard Charles, SDSC
John Volakis, Edward Davidson, University of Michigan
Jack Lancaster, University of Texas Medical Center at San Antonio

Programming Tools and Environments

Linear Algebra, Meta-Chaos,
KeLP, Data Fusion
Interaction Environments
Visualization Tools

person's ears serve two goals--first, to hear sounds, and second, to locate where a sound coming from. A hearing aid helps with the first goal by making sounds louder, but it does not help locate the source of a sound. To do so, a hearing aid would have to take into account how the outer ear makes changes to sounds before they strike the eardrum. A team of engineers led by Leszek Demkowicz at the University of Texas is developing software for acoustic and electromagnetic simulations that, in one form, may help model how the ear locates sounds while, in a different form, will help improve the antennas and radar signals for Air Force jets. Both problems require the power of high-performance computers to produce realistic simulations.





The difference in the examples above is the type of signal--acoustic waves for the ear and electromagnetic fields for the aircraft radar. The mathematical differences are enough to require Demkowicz's team to develop separate codes for acoustics problems and electromagnetics problems. On the other hand, both problems share the common feature that the object being studied must be represented as a model, called a grid or mesh, constructed from thousands of building blocks. The mesh for the human head, especially if the brain is included, is actually much more complicated than that of an aircraft.

However, the codes do not care about the shape of the mesh. Therefore, engineers can study acoustic waves around other vehicles such as submarines, for example, or electromagnetic waves, such as those from cellular phones, around the human head. Over the course of developing the codes, Demkowicz has studied all of these problems.

"We have developed the techniques and codes for small problems on workstations," said Demkowicz, assistant director of the Texas Institute for Computational and Applied Mathematics (TICAM) and leader of the Electromagnetic and Acoustic Fields project in the Engineering thrust area. "The challenge that we are addressing through NPACI is to do large problems on parallel computers."

The technique that makes realistic simulations possible goes by the name hp-adaptive methods. In such methods, the simulation is able to change, or adapt, both the size of the original mesh and the order of approximation as it proceeds toward a solution. The adaptive methods allow simulations to reach more accurate predictions, but for large problems and complex meshes, the methods extract a heavy computational toll. (For more on the development of hp-adaptive methods, see the April-June 1998 enVision.)

Demkowicz's team is producing four codes to apply these methods to a variety of situations. Currently on the Web, are 2Dhp90 and 2Dhp90_EM. Both are 2-D hp-adaptive methods written in Fortran 90. The first is a general-purpose code, developed by Demkowicz, Timothy Walsh, Andrzej Bajer, and Satish Chavva, for problems such as acoustics. The second is specifically for electromagnetics problems and was developed by Demkowicz and Waldek Rachowicz. A second pair of codes, 3Dhp90 and 3Dhp90_EM, extends the methods to 3-D meshes; these codes should be available on the Web within a few months, according to Demkowicz (Figure 1).

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AFigure 1a - Adaptive Finite Elements

BFigure1b - Adaptive Finite Elements

CFigure C - Adaptive Finite Elements

DFigure 1d - Adaptive Finite Elements

Figure 1. Adaptive Finite Elements
These examples of adaptive finite elements for electromagnetics all show an underlying adaptive grid to solve the problem. A: The y-component of the electric field for two cylinders of dissimilar media. B: Real part of the x-component of the field for a scattering wave-guide problem. C: The y-component of the electric field for a shielded single microstrip line. D: The imaginary part of the y-component of the scattered electric field from a plane wave on a double wedge.



The next major work on the codes, supported by NPACI, will be to parallelize the computationally intensive portion for distributed memory parallel machines such as the IBM SP and CRAY T3E. In the terminology of adaptive methods, Demkowicz and his team are focusing on the "solver" component of the application. In this effort, they are collaborating with James Demmel of UC Berkeley, the leader of the Linear Algebra project from the Programming Tools and Environments thrust area (Figure 2).

An adaptive code has a few general steps: First, generate an initial mesh. Second, solve the problem on the mesh; the solver step is the most demanding. Then on the solved mesh, estimate the error, adapt the mesh, and repeat the solver step until the results are below the error tolerance. Eventually, all of these steps will be bundled into one parallel code. But currently, the group's efforts are focused on the solver, which Demkowicz intends to have completed later this year.

"Even on 2-D problems, the solver component becomes computationally demanding for large problems," Demkowicz said. "We have completed and tested the two major components of the solver on problems with up to 1 million degrees of freedom." The team still faces hours of manual data movement between a workstation that runs the serial code steps and the parallel machines that run the parallel solver.

The parallel approach they have implemented involves a static decomposition of the mesh, which allows them to tackle larger problems. However, a static decomposition may not always be the most efficient way to break the problem into pieces. To support dynamically changing unstructured grids, Demkowicz has initiated efforts with several projects from the Programming Tools and Environments thrust area: Meta-Chaos, led by Joel Saltz of Johns Hopkins University and the University of Maryland; KeLP, led by Scott Baden of UC San Diego; and the Scalable Dynamic Distributed Array (SDDA) work of James Browne at the University of Texas.

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Figure 2 - Electromagnetic Field Simulations
Figure 2. Electromagnetic Field Simulations
The two-grid solver for time-harmonic Maxwell's equations showing an actual, h-adaptive grid and the corresponding coarse grid.

Figure 3. The Ear Problem
A mesh for the ear problem, courtesy of Richard Charles of SDSC, and a corresponding domain decomposition obtained using Metis.
Figure 3 - domain decompositionFigure 3 - mesh for ear problem


Demkowicz is developing the adaptive methods codes as part of several ongoing engineering projects. A three-month-old project with Richard Charles of SDSC is simulating the acoustic waves around the human head to understand better how the shape of the pinna--the part of the ear outside the head--and the ear canal contribute to the brain's ability to locate the source of a sound (Figure 3).

"By modeling the normal hearing process, hearing aids will be able to incorporate more sophisticated cues," Charles said. Demkowicz's codes, still in serial form, will be parallelized and used to simulate how a sound propagates from a source through the outer, middle, and inner ear until the nerves pick up the signal. The collaboration between SDSC and Texas has also been identified as a Ph.D. project for Walsh of Demkowicz's team.

The second project is addressing the larger problem of the entire head--developing accurate predictions of acoustic waves and electromagnetic fields in and around the human head. While the codes are in place and have been tested on hypothetical meshes of heads, the simulations will be most useful when they can be run on meshes based on actual data collected on human heads.

To construct such meshes, Demkowicz is collaborating with Jack Lancaster at the University of Texas Medical Center at San Antonio and Martin Rumpf from the University of Bonn, Germany. A simplified model is being developed in a collaboration with Niels Kuster and his Laboratory for EMF and Microwave Electronics in Zurich, Switzerland. The simulations are to be compared with extensive experimental data produced by Kuster's lab, which specializes in testing cellular phones. To produce the meshes, Demkowicz is working with Chandrajit Bajaj, director of TICAM's Center for Computational Visualization and leader of the Visualization Tools project in the Interaction Environments thrust area.

Finally, Demkowicz has a number of ongoing collaborations with the Air Force, which are now looking at 3-D antenna and scattering problems. In fact, these problems are more tractable than the head problem because the meshes are much less complex. On this application, Demkowicz is collaborating with a team led by John Volakis at the University of Michigan.

"Our work with the Texas group helps both of us improve our codes for parallel performance," said Volakis, a professor in the Department of Electrical Engineering and Computer Science at Michigan. "Even though we're using different formulations, we have learned from each other how best to implement parts of our codes. I've learned from him about how the hp-adaptive methods work, and he's learned from our work and mature codes on large-scale solvers."

Volakis's team is using hybrid finite-element methods to perform large-scale simulations of radar and antenna imaging, and the two groups are working together to improve their methods and evaluate the accuracy of the predictions. Volakis's team is using IBM and SGI machines at Michigan and the HP V2000 at Caltech.

"Together, these projects are developing the infrastructure to solve large 3-D problems of this kind," Demkowicz said. "We hope to assemble the solver pieces by the end of the summer, and once the entire code can run on one machine, it could revolutionize the process of conducting such engineering simulations." --DHend note

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