| Title: |
On the Computation of Square Roots and Inverse Square Roots of Gram Matrices for Surface Integral Equations in Electromagnetics |
| Authors: |
Chen, Rui; Merlini, Adrien; Andriulli, Francesco, P |
| Contributors: |
Politecnico di Torino = Polytechnic of Turin (Polito); Département Micro-Ondes (IMT Atlantique - MO); IMT Atlantique (IMT Atlantique); Institut Mines-Télécom Paris (IMT)-Institut Mines-Télécom Paris (IMT); Equipe PIM (Lab-STICC_PIM); Laboratoire des sciences et techniques de l'information, de la communication et de la connaissance (Lab-STICC); École Nationale d'Ingénieurs de Brest (ENIB); Université de Brest (UBO EPE)-Institut National Polytechnique de Bretagne (Bretagne INP)-Université de Brest (UBO EPE)-Institut National Polytechnique de Bretagne (Bretagne INP)-Université de Bretagne Sud (UBS)-Centre National de la Recherche Scientifique (CNRS)-IMT Atlantique (IMT Atlantique); Institut Mines-Télécom Paris (IMT)-Institut Mines-Télécom Paris (IMT)-École Nationale Supérieure de Techniques Avancées (ENSTA); Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris)-École Nationale d'Ingénieurs de Brest (ENIB); Institut Polytechnique de Paris (IP Paris)-Institut Polytechnique de Paris (IP Paris); This work has received support from the National Natural Science Foundation of China (NSFC) under Grant 62201264 and Grant 62331016, from the Fundamental Research Funds for the Central Universities under Grant30924010207, from the Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Province under Grant 20240063, from the Foundation of Anhui Key Laboratory of Industrial Energy-Savingand Safety under Grant KFKT202306, from the European Innovation Council (EIC) through the European Union’s Horizon Europe research Programme under Grant 101046748 (Project CEREBRO), by the European Union –Next Generation EU within the PNRR project “Multiscale modeling and Engineering Applications” of the Italian National Center for HPC, Big Data and Quantum Computing (Spoke 6) – PNRR M4C2, Investimento 1.4 - Avviso n. 3138 del 16/12/2021 - CN00000013 National Centre for HPC, Big Data and Quantum Computing (HPC) - CUP E13C22000990001, and has received a French government support granted to the Labex CominLabs excellence laboratory and managed by the National Research Agency in the “Investing for the Future” program under reference ANR-10-LABX-07-01 (project “CYCLE”). |
| Source: |
ISSN: 0018-926X ; IEEE Transactions on Antennas and Propagation ; https://hal.science/hal-05087045 ; IEEE Transactions on Antennas and Propagation, In press, ⟨10.1109/tap.2025.3568083⟩. |
| Publisher Information: |
CCSD; Institute of Electrical and Electronics Engineers |
| Publication Year: |
2025 |
| Collection: |
Université de Bretagne Occidentale: HAL |
| Subject Terms: |
Gram matrix; matrix function; polynomial expansion; spectral analysis; surface integral equation; [SPI.ELEC]Engineering Sciences [physics]/Electromagnetism; [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] |
| Description: |
International audience ; Surface integral equations (SIEs) are widely used for modeling electromagnetic scattering problems. However, after their discretization via the boundary element method, the spectra and eigenvectors of resulting matrices are not usually representative of those of underlying surface integral operators, which can be problematic for methods that rely heavily on spectral properties. To address this issue, the spectrum of the integral operators can be recovered, while preserving symmetry, using square roots and inverse square roots of Gram matrices. In this work, several algorithms are delineated for the computation of square roots and inverse square roots of several relevant Gram matrices. The algorithms we detail rely on properly chosen polynomial expansions of the scalar square root and inverse square root functions and the theory of matrix functions. Tables containing different sets of expansion coefficients are provided along with comparative numerical experiments that evidence advantages and disadvantages of the different approaches. In addition, the use of the proposed techniques as a tool for the recovery of the spectrum of integral operators is illustrated in the case of a spherical geometry for which the analytic spectrum is known. |
| Document Type: |
article in journal/newspaper |
| Language: |
English |
| DOI: |
10.1109/tap.2025.3568083 |
| Availability: |
https://hal.science/hal-05087045; https://hal.science/hal-05087045v1/document; https://hal.science/hal-05087045v1/file/CommunicationOn_the_Computation_of_Square_Roots_and_Inverse_Square_Roots_of_Gram_Matrices_for_Surface_Integral_Equations_in_Electromagnetics.pdf; https://doi.org/10.1109/tap.2025.3568083 |
| Rights: |
http://creativecommons.org/licenses/by/ ; info:eu-repo/semantics/OpenAccess |
| Accession Number: |
edsbas.43ADE26E |
| Database: |
BASE |