H-Matrix Accelerated Direct Matrix Solver for Maxwell’s Equations Using the Chebyshev-Based Nyström Boundary Integral Equation Method
An H-matrix accelerated direct solver employing the high-order Chebyshev-based Boundary Integral Equation (CBIE) method has been formulated, tested, and profiled for performance on high contrast dielectric materials and electrically large perfect electric conductor objects. The matrix fill performan...
Saved in:
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2025-01-01
|
| Series: | IEEE Open Journal of Antennas and Propagation |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/10734393/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832576792856100864 |
|---|---|
| author | Jin Hu Emrah Sever Omid Babazadeh Ian Jeffrey Vladimir Okhmatovski Constantine Sideris |
| author_facet | Jin Hu Emrah Sever Omid Babazadeh Ian Jeffrey Vladimir Okhmatovski Constantine Sideris |
| author_sort | Jin Hu |
| collection | DOAJ |
| description | An H-matrix accelerated direct solver employing the high-order Chebyshev-based Boundary Integral Equation (CBIE) method has been formulated, tested, and profiled for performance on high contrast dielectric materials and electrically large perfect electric conductor objects. The matrix fill performance of the CBIE proves to be fast for small to moderately sized problems compared to its counterparts, e.g., the locally corrected Nyström (LCN) method, due to the way it handles the singularities by means of a global change of variable method. However, in the case of electrically large scattering problems, the matrix fill and factorization still dominate the solution time when using a direct solution approach. To address this issue, an H-Matrix framework is employed, effectively resolving the challenge and establishing the CBIE as a competitive high-order method for solving scattering problems with poorly conditioned matrix equations. The efficacy of this approach is demonstrated through extensive numerical results, showcasing its robustness to problems that are electrically large, near physical resonances, or that have large dielectric permittivities. The capability of the proposed solver for handling arbitrary geometries is also demonstrated by considering various scattering examples from complex CAD models. |
| format | Article |
| id | doaj-art-e847a7454cc14be9a94d5996432c89e0 |
| institution | Kabale University |
| issn | 2637-6431 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Open Journal of Antennas and Propagation |
| spelling | doaj-art-e847a7454cc14be9a94d5996432c89e02025-01-31T00:02:12ZengIEEEIEEE Open Journal of Antennas and Propagation2637-64312025-01-016117118010.1109/OJAP.2024.348581710734393H-Matrix Accelerated Direct Matrix Solver for Maxwell’s Equations Using the Chebyshev-Based Nyström Boundary Integral Equation MethodJin Hu0https://orcid.org/0000-0001-6705-3455Emrah Sever1https://orcid.org/0000-0001-8221-6160Omid Babazadeh2https://orcid.org/0000-0003-2798-9309Ian Jeffrey3https://orcid.org/0000-0003-1312-3248Vladimir Okhmatovski4https://orcid.org/0000-0002-1688-3691Constantine Sideris5https://orcid.org/0000-0002-3042-4889Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USAElectromagnetic Analysis Team, ASELSAN Inc., Ankara, TürkiyeDepartment of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB, CanadaDepartment of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB, CanadaDepartment of Electrical and Computer Engineering, University of Manitoba, Winnipeg, MB, CanadaDepartment of Electrical and Computer Engineering, University of Southern California, Los Angeles, CA, USAAn H-matrix accelerated direct solver employing the high-order Chebyshev-based Boundary Integral Equation (CBIE) method has been formulated, tested, and profiled for performance on high contrast dielectric materials and electrically large perfect electric conductor objects. The matrix fill performance of the CBIE proves to be fast for small to moderately sized problems compared to its counterparts, e.g., the locally corrected Nyström (LCN) method, due to the way it handles the singularities by means of a global change of variable method. However, in the case of electrically large scattering problems, the matrix fill and factorization still dominate the solution time when using a direct solution approach. To address this issue, an H-Matrix framework is employed, effectively resolving the challenge and establishing the CBIE as a competitive high-order method for solving scattering problems with poorly conditioned matrix equations. The efficacy of this approach is demonstrated through extensive numerical results, showcasing its robustness to problems that are electrically large, near physical resonances, or that have large dielectric permittivities. The capability of the proposed solver for handling arbitrary geometries is also demonstrated by considering various scattering examples from complex CAD models.https://ieeexplore.ieee.org/document/10734393/Computational electromagneticsboundary integral equationNyström methodH-matricesfast direct solver |
| spellingShingle | Jin Hu Emrah Sever Omid Babazadeh Ian Jeffrey Vladimir Okhmatovski Constantine Sideris H-Matrix Accelerated Direct Matrix Solver for Maxwell’s Equations Using the Chebyshev-Based Nyström Boundary Integral Equation Method IEEE Open Journal of Antennas and Propagation Computational electromagnetics boundary integral equation Nyström method H-matrices fast direct solver |
| title | H-Matrix Accelerated Direct Matrix Solver for Maxwell’s Equations Using the Chebyshev-Based Nyström Boundary Integral Equation Method |
| title_full | H-Matrix Accelerated Direct Matrix Solver for Maxwell’s Equations Using the Chebyshev-Based Nyström Boundary Integral Equation Method |
| title_fullStr | H-Matrix Accelerated Direct Matrix Solver for Maxwell’s Equations Using the Chebyshev-Based Nyström Boundary Integral Equation Method |
| title_full_unstemmed | H-Matrix Accelerated Direct Matrix Solver for Maxwell’s Equations Using the Chebyshev-Based Nyström Boundary Integral Equation Method |
| title_short | H-Matrix Accelerated Direct Matrix Solver for Maxwell’s Equations Using the Chebyshev-Based Nyström Boundary Integral Equation Method |
| title_sort | h matrix accelerated direct matrix solver for maxwell x2019 s equations using the chebyshev based nystr x00f6 m boundary integral equation method |
| topic | Computational electromagnetics boundary integral equation Nyström method H-matrices fast direct solver |
| url | https://ieeexplore.ieee.org/document/10734393/ |
| work_keys_str_mv | AT jinhu hmatrixaccelerateddirectmatrixsolverformaxwellx2019sequationsusingthechebyshevbasednystrx00f6mboundaryintegralequationmethod AT emrahsever hmatrixaccelerateddirectmatrixsolverformaxwellx2019sequationsusingthechebyshevbasednystrx00f6mboundaryintegralequationmethod AT omidbabazadeh hmatrixaccelerateddirectmatrixsolverformaxwellx2019sequationsusingthechebyshevbasednystrx00f6mboundaryintegralequationmethod AT ianjeffrey hmatrixaccelerateddirectmatrixsolverformaxwellx2019sequationsusingthechebyshevbasednystrx00f6mboundaryintegralequationmethod AT vladimirokhmatovski hmatrixaccelerateddirectmatrixsolverformaxwellx2019sequationsusingthechebyshevbasednystrx00f6mboundaryintegralequationmethod AT constantinesideris hmatrixaccelerateddirectmatrixsolverformaxwellx2019sequationsusingthechebyshevbasednystrx00f6mboundaryintegralequationmethod |