强激光与粒子束2024，Vol.36Issue(7)：35-42,8.DOI:10.11884/HPLPB202436.240076
电磁场B样条间断有限元方法
B-spline discontinuous Galerkin method for Maxwell's equations
摘要
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.关键词
B样条/间断有限元/瞬态电磁学/高阶精度/畸变网格Key words
B-spline/discontinuous finite element/transient electromagnetics/high-order accuracy/distorted grid分类
数理科学引用本文复制引用
华沁怡,李林,齐红新..电磁场B样条间断有限元方法[J].强激光与粒子束,2024,36(7):35-42,8.基金项目
国家重点研发计划(2020YFA0709800) （2020YFA0709800）
国家自然科学基金项目(12192251、12274134) （12192251、12274134）
上海市教委基金项目(2023ZKZD35) （2023ZKZD35）
