Efficient ray-tracing procedure for radio wave propagation modeling using homogeneous geometric algebra

Abstract

ABSTRACT Ray-tracing is an efficient asymptotic computational electromagnetic method for studying wave propagation. The major bottleneck of ray-tracing algorithms is the computational complexity of the geometric-processing steps. There is a clear need for designing efficient ray-tracing algorithms and implementations in computational electromagnetics applications. We use Geometric algebra for the formulation of the pre-processing of electromagnetic ray tracing. Geometric algebra provides unified mathematical representations of geometric primitives and transformations. Various kinds of geometric algebras are currently used in many practical applications. We develop a unified 2D/3D ray-tracing procedure based on the homogeneous geometric algebra. The procedure is implemented using generative programming for optimizing code compilation. Results show that combining the powerful mathematical modeling capabilities of geometric algebra with efficient automatic code generation resulted in better performance of the ray-tracing implementation compared to typical approaches.