Solvers for Large Integral and PDE Computations

By Dr. John Volakis

Department of Electrical Engineering & Computer Science
University of Michigan
Ann Arbor, MI 48109-2122


Over the past few years hybrid finite element methods (FEM) have been successfully applied to a variety of scattering, antenna and propagation analysis problems. Much of the methods' attractiveness over other approaches is attributed to the geometrical adaptability, material generality and low memory requirements of the FEM. These same attributes also make hybrid FEM methods equally attractive for printed antennas and microwave circuit simulations. Most recently several three-dimensional FEM implementations have been presented for these applications.

This presentation will give an overview of the currently employed and upcoming solvers for hybrid finite element-boundary integral systems whose rank maybe on the order of 0.5 to several million unknowns for practical simulations. These systems are partly sparse and partly dense, and present us with unique challenges. Their efficient solution is nevertheless crucial to radar imaging, target identification, smart antenna designs and for wireless communications systems. At this moment, several direct and iterative approaches are being considered. The merits of these solvers need to be evaluated in terms of their efficient implementation on various computing platforms. The recent introduction of fast integral methods has certainly impacted our thinking of iterative solvers. These methods promise to reduce the CPU and memory requirements down to O(N1.3) or even down to O(N log N), where N represents the degrees of freedom. The validity of these claims will be examined by looking at large scale implementation involving new reconfigurable conformal antennas whose design was made possible with such algorithms. We will also show performance of two recent LU solvers on parallel platforms for radar scattering simulations of full scale airframe configurations.

To Be Presented At The

Forum On Numerical Methods for
Partial Differential Equations

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