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A Hybrid CM-BEM Formulation for Solving Large-Scale 3D Eddy-Current Problems Based on ℋ-Matrices and Randomized Singular Value Decomposition for BEM Matrix Compression

Author

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  • Federico Moro

    (Dipartimento di Ingegneria Industriale, Università degli Studi di Padova, 35131 Padova, Italy)

  • Lorenzo Codecasa

    (Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, 20133 Milano, Italy)

Abstract

We present a novel a , v - q hybrid method for solving large-scale time-harmonic eddy-current problems. This method combines a hybrid unsymmetric formulation based on the cell method and the boundary element method with a hierarchical matrix-compression technique based on randomized singular value decomposition. The main advantage is that the memory requirements are strongly reduced compared to the corresponding hybrid method without matrix compression while retaining the same robust solution strategy consisting of a simple construction of the preconditioner. In addition, the matrix-compression accuracy and efficiency are enhanced compared to traditional compression methods, such as adaptive cross approximation. The numerical results show that the proposed hybrid approach can also be effectively used to analyze large-scale eddy-current problems of engineering interest.

Suggested Citation

  • Federico Moro & Lorenzo Codecasa, 2023. "A Hybrid CM-BEM Formulation for Solving Large-Scale 3D Eddy-Current Problems Based on ℋ-Matrices and Randomized Singular Value Decomposition for BEM Matrix Compression," Mathematics, MDPI, vol. 11(6), pages 1-30, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1324-:d:1092232
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    References listed on IDEAS

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    1. Federico Moro & Lorenzo Codecasa, 2021. "Coupling the Cell Method with the Boundary Element Method in Static and Quasi–Static Electromagnetic Problems," Mathematics, MDPI, vol. 9(12), pages 1-30, June.
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