## University of Kentucky

# New Image Compression Algorithm for Fast Electromagnetic Simulations

## Institution

University of Kentucky

## Faculty Advisor/ Mentor

Robert Adams

## Abstract

Many electromagnetic related problems are too complex to solve using traditional analytical methods. Computational methods have been developed that transform the differential or integral equations that describe the problem to a set of linear equations. This set of equations can then be solved using well known linear algebraic techniques. Computer simulation of real-world electromagnetic problems involving large objects positioned in three spatial dimensions often require prohibitive amounts of computer resources in terms of memory and processor time. For most systems it is required to simplify the problem by using a course surface sample density or by reducing the problem to one or two dimensions. In this project we demonstrate that the required computational resources can be reduced by employing an image compression algorithm. The compression algorithm we have developed is built around a formulation of the scattering problem obtained via Green's theorem as a field propagator. Singular value decompositions are applied to the resulting angular-space matrix in a novel way in order to form and separate radiating modes and to form beams which radiate to specific angular regions in the far field. A multiresolution version of the compression algorithm is obtained by forming beams that radiate to successively larger angular regions. Finally, the resulting beam transforms are used to determine a sparse matrix representation of the electromagnetic problem. Preliminary work with two dimensional geometries shows that an increase of problem size of two orders of magnitude is possible by using this image compression technique.

New Image Compression Algorithm for Fast Electromagnetic Simulations

Many electromagnetic related problems are too complex to solve using traditional analytical methods. Computational methods have been developed that transform the differential or integral equations that describe the problem to a set of linear equations. This set of equations can then be solved using well known linear algebraic techniques. Computer simulation of real-world electromagnetic problems involving large objects positioned in three spatial dimensions often require prohibitive amounts of computer resources in terms of memory and processor time. For most systems it is required to simplify the problem by using a course surface sample density or by reducing the problem to one or two dimensions. In this project we demonstrate that the required computational resources can be reduced by employing an image compression algorithm. The compression algorithm we have developed is built around a formulation of the scattering problem obtained via Green's theorem as a field propagator. Singular value decompositions are applied to the resulting angular-space matrix in a novel way in order to form and separate radiating modes and to form beams which radiate to specific angular regions in the far field. A multiresolution version of the compression algorithm is obtained by forming beams that radiate to successively larger angular regions. Finally, the resulting beam transforms are used to determine a sparse matrix representation of the electromagnetic problem. Preliminary work with two dimensional geometries shows that an increase of problem size of two orders of magnitude is possible by using this image compression technique.