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

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 u...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-05, Vol.12 (10), p.1565
Main Authors: García, Eliseo, Delgado, Carlos, Cátedra, Felipe
Format: Article
Language:English
Subjects:
Accuracy
Approximation
Basis functions
Computation
computational electromagnetics
Decomposition
Electromagnetism
Fourier transforms
full-wave analysis
Iterative solution
macro basis functions
Methods
moment methods
Multipoles
numerical methods
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12101565