
Research Activities

Parallelization of MLFMA
Fast and accurate solutions of largescale scattering problems involving threedimensional closed conductors with arbitrary shapes are possible using the multilevel fast multipole algorithm (MLFMA). With an efficient parallelization of MLFMA, scattering problems that are discretized with tens of millions of unknowns are easily solved on a cluster of computers. We extensively investigate the parallelization of MLFMA, identify the bottlenecks, and provide remedial procedures to improve the efficiency of the implementations. The accuracy of the solutions is demonstrated on a scattering problem involving a sphere of radius 110 lambda discretized with 41,883,638 unknowns, the largest integralequation problem solved to date. In addition to canonical problems, we also present the solution of reallife problems involving complicated targets with large dimensions. click for more...
 Solutions of Electromagnetics Problems Involving Tens of Millions of Unknowns
By achieving the parallelization of MLFMA, which is not trivial at all, we have been able to solve extremely large electromagnetics problems involving tens of millions of unknowns. Since we are using carefully formulated integral equations, the solutions are not only efficient, but also accurate. Hence, accurate solutions of previously unsolvable problems are useful both in reallife applications and for benchmarking purposes. Each solved problem involving tens of millions of unknowns was the largest of its class (hence, a world record) at the time. Examples of solutions of such extremely large problems are presented here.

Hierarchical Parallelization of MLFMA
We developed a novel hierarchical partitioning strategy for the efficient parallelization of the multilevel fast multipole algorithm (MLFMA) on distributedmemory architectures to solve largescale problems in electromagnetics. Unlike previous parallelization techniques, the tree structure of MLFMA is distributed among processors by partitioning both clusters and samples of fields at each level. Due to the improved loadbalancing, the hierarchical strategy offers a higher parallelization efficiency than previous approaches, especially when the number of processors is large. We demonstrate the improved efficiency on scattering problems discretized with millions of unknowns. In addition, we present the effectiveness of our algorithm by solving very large scattering problems involving a conducting sphere of radius 210 wavelengths and a complicated reallife target with a maximum dimension of 880 wavelengths. Both of the objects are discretized with more than 200 million unknowns. click for more...

Solutions of Electromagnetics Problems Involving Hundreds of Millions of Unknowns
Accurate simulations of reallife electromagnetics problems with integral equations require the solution of dense matrix equations involving millions of unknowns. Solutions of these extremely large problems cannot be achieved
easily, even when using the most powerful computers with stateoftheart technology. Hence, many electromagnetics
problems in the literature have been solved by resorting to various approximation techniques without controllable
error. In this paper, we present fullwave solutions of scattering problems discretized with hundreds of millions
of unknowns by employing a parallel implementation of the multilevel fast multipole algorithm. Various examples
involving canonical and complicated objects are presented in order to demonstrate the feasibility of accurately solving
largescale problems on relatively inexpensive computing platforms.click for more...

Approximate Multilevel Fast Multipole Algorithm (AMLFMA) as a Preconditioner
An iterative innerouter scheme for the efficient solution of largescale electromagnetics problems involving perfectlyconducting objects formulated with surface integral equations. Problems are solved by employing the multilevel fast multipole algorithm (MLFMA) on parallel computer systems. In order to construct a robust preconditioner, we develop an approximate MLFMA (AMLFMA) by systematically increasing the efficiency of the ordinary MLFMA. Using a flexible outer solver, iterative MLFMA solutions are accelerated via an inner iterative solver, employing AMLFMA and serving as a preconditioner to the outer solver. The resulting implementation is tested on various electromagnetics problems involving both open and closed conductors. We show that the processing time decreases significantly using the proposed method, compared to the solutions obtained with conventional preconditioners in the literature. click for more...

Computational Study of Scattering From Healthy and Diseased Red Blood Cells
Comparative study of scattering from healthy red blood cells (RBCs) and diseased
RBCs with deformed shapes. Scattering problems involving threedimensional RBCs are formulated
accurately with the electric and magnetic current combinedfield integral equation and solved
efficiently by the multilevel fast multipole algorithm. We compare scattering cross section values
obtained for different RBC shapes and different orientations. This way, we determine strict guidelines
to distinguish deformed RBCs from healthy RBCs and to diagnose various diseases using
scattering cross section values. The results may be useful for designing new and improved flow
cytometry procedures. click for more...

Numerical Techniques:
 Modeling of complicated geometries on computers
 Development of flexible simulation environments
 Development of powerful software packages
 Fast solvers (both frequencydomain and timedomain solvers)
 Fast multipole method (FMM)
 Finitedifference timedomain (FDTD)
 Method of moments (MoM)
 Fast solution of nearresonant structures
 ntegrating inhouse software packages with other commercial software
 Modeling EM phenomena using circuittheory concepts by employing parasitic extraction, AWE, and SPICE.

Radars:
 RCS (Radar Cross Section) computations (and measurements)
 Stealth studies
 GPR (Ground Penetrating Radar) simulations
 EM scattering from targets with arbitrary geometries, such as aircraft, missiles, ships, any electronic equipment and furniture in a room, human forms, buildings, and geographical features

EMC (Electromagnetic Compatibility):
 Simulations
 Measurements (precompliance and compliance)
 Military and commercial EMC standards
 EMC education
 Measurement of GSM base stations
 Radiation from PCB and chip geometries
 Crosstalk and signalintegrity issues
 Radiation from and coupling through apertures on enclosures and shields

Antennas:
 Frequencyindependent (broadband) antenna design
 Antennas installed on platforms (aircraft, ships, satellites, telephones)
 Printed antennas, conformal antennas (GPS, aircraft, missile, GSM)
 Antenna measurements
 Radiation from antenna structures, computation of antenna patterns
 Synthesis of broadband antennas and antenna arrays
