Use of the Adaptive Cross Approximation for the Efficient Computation of the Reduced Matrix with the Characteristic Basis Function Method

Eliseo García (), Carlos Delgado () and Felipe Cátedra
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Eliseo García: Departamento de Automática, Universidad de Alcalá, 28801 Alcalá de Henares, Spain
Carlos Delgado: Departamento de Ciencias de la Computación, Universidad de Alcalá, 28801 Alcalá de Henares, Spain
Felipe Cátedra: Departamento de Ciencias de la Computación, Universidad de Alcalá, 28801 Alcalá de Henares, Spain

Mathematics, 2024, vol. 12, issue 10, 1-10

Abstract: A technique for the reduction in the CPU-time in the analysis of electromagnetic problems using the Characteristic Basis Function Method (CBFM) is presented here, allowing for analysis of electrically large cases where an iterative solution process cannot be avoided. This technique is based on the use of the Adaptive Cross Approximation (ACA) for the fast computation of the coupling matrix between CBFs belonging to adjacent blocks, as well as the Multilevel Fast Multipole Method (MLFMM) for the computation of matrix−vector products in the solution of the full system. This combination allows for a noticeable reduction in the computational resources during the analysis of electrically large and complex scenarios while maintaining a very good degree of accuracy. A number of test cases serve to validate the presented approach in terms of accuracy, memory and CPU-time compared with conventional techniques.

Keywords: computational electromagnetics; numerical methods; full-wave analysis; moment methods; macro basis functions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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