Boundary Conditions Comparison for Electromagnetic Simulation Using the Finite Element Method with CUDA Computing

The Finite Element Method (FEM) is a widely recognized technique for solving boundary value problems in the design and analysis of RF (Radio Frequency) components, such as waveguides. In the process of analyzing such structures using FEM, the traditionally infinite analysis domain is required to be truncated to a finite domain. This necessitates the incorporation of appropriate artificial boundaries to truncate the analysis domain, which should ideally occupy the smallest possible region. Renowned boundary conditions in this context include ABC (Absorbing Boundary Conditions), WPBC (Wave Port Boundary Conditions), and PML (Perfectly Matched Layers), each presenting its own set of advantages and drawbacks. This paper applies these boundary conditions in the analysis of a rectangular waveguide containing inhomogeneity, leveraging a tailored FEM solution implemented in MATLAB (Matrix Laboratory). The accuracy of the FEM solutions is meticulously compared and validated against results from the commercial electromagnetic software HFSS, affirming the robustness and reliability of the findings. Additionally, the proficiencies of the CUDA (Compute Unified Device Architecture) MATH library and kernel function within the CUDA Toolkit are harnessed to execute parallel analysis of the linear systems formulated by the FEM. A detailed performance comparison between MATLAB's backslash operator and the CUDA-accelerated approach is conducted.