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.

中文翻译：

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使用齐次几何代数进行无线电波传播建模的高效射线追踪程序

摘要 射线追踪是研究波传播的一种有效的渐近计算电磁方法。光线追踪算法的主要瓶颈是几何处理步骤的计算复杂性。显然需要在计算电磁学应用中设计有效的光线追踪算法和实现。我们使用几何代数来制定电磁射线追踪的预处理。几何代数提供几何基元和变换的统一数学表示。目前在许多实际应用中使用了各种几何代数。我们基于齐次几何代数开发了统一的 2D/3D 光线追踪程序。该过程是使用生成式编程来实现的，以优化代码编译。