B-spline discontinuous Galerkin method for Maxwell’s equations

Hua Qinyi; Li Lin; Qi Hongxin

doi:10.11884/HPLPB202436.240076

Volume 36 Issue 7

May 2024

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Hua Qinyi, Li Lin, Qi Hongxin. B-spline discontinuous Galerkin method for Maxwell’s equations[J]. High Power Laser and Particle Beams, 2024, 36: 073004. doi: 10.11884/HPLPB202436.240076

Citation:

Hua Qinyi, Li Lin, Qi Hongxin. B-spline discontinuous Galerkin method for Maxwell’s equations[J]. High Power Laser and Particle Beams, 2024, 36: 073004. doi: 10.11884/HPLPB202436.240076

Hua Qinyi, Li Lin, Qi Hongxin. B-spline discontinuous Galerkin method for Maxwell’s equations[J]. High Power Laser and Particle Beams, 2024, 36: 073004. doi: 10.11884/HPLPB202436.240076

Citation:

Hua Qinyi, Li Lin, Qi Hongxin. B-spline discontinuous Galerkin method for Maxwell’s equations[J]. High Power Laser and Particle Beams, 2024, 36: 073004. doi: 10.11884/HPLPB202436.240076

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B-spline discontinuous Galerkin method for Maxwell’s equations

doi: 10.11884/HPLPB202436.240076

Hua Qinyi^1
,,
Li Lin¹,
Qi Hongxin^{2
,
,}

1.
State Key Laboratory of Precision Spectroscopy , East China Normal University, Shanghai 200241, China
2.
School of Physics and Electronic Science, East China Normal University, Shanghai 200241, China

Received Date: 2024-03-06
Accepted Date: 2024-04-07
Rev Recd Date: 2024-04-07

Available Online: 2024-04-19

Publish Date: 2024-05-31

Abstract

Abstract

In the field of computational electromagnetics, the discontinuous Galerkin time domain (DGTD) method typically relies on irregular grid partitioning in model space and high-order polynomial interpolation calculations on elements. When comparing two-dimensional spatial quadrilateral mesh partitioning to triangular mesh partitioning at the same interpolation order, quadrilateral meshing offers fewer degrees of freedom and higher computational efficiency. However, traditional basis function spaces, relying on isoparametric transformations and polynomial tensor product interpolation, only possess low-order completeness on quadrilateral elements. Consequently, their stability and accuracy are significantly influenced by grid distortion. To address this challenge, this thesis proposes a high-order B-spline interpolation DGTD method based on irregular quadrilateral meshes for solving Maxwell's equations. The advantage of B-spline interpolation lies in its high-order completeness on irregular elements, effectively eliminating internal degrees of freedom within the elements. Furthermore, the coefficient matrices of the discrete system for Maxwell's equations also possess exact analytical forms. Analyzing the eigenmodes of cavities and the electromagnetic scattering of wedge structures, thus the maximum allowable time step increasing by 2.5 times and reducing the required unknowns by 25% compared to COMSOL software, the proposed algorithm exhibits notable advantages in terms of higher stability and precision.
- B-spline,
- discontinuous finite element,
- transient electromagnetics,
- high-order accuracy,
- distorted grid

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References(16)

References

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