离散化
数学
应用数学
麦克斯韦方程组
稳健性(进化)
间断伽辽金法
基函数
计算电磁学
边值问题
电磁场求解器
区域分解方法
伽辽金法
有限元法
数学分析
电磁场
量子力学
非齐次电磁波方程
生物化学
热力学
基因
物理
光场
化学
作者
Jan S. Hesthaven,Tim Warburton
标识
DOI:10.1006/jcph.2002.7118
摘要
We present a convergent high-order accurate scheme for the solution of linear conservation laws in geometrically complex domains. As our main example we include a detailed development and analysis of a scheme for the time-domain solution of Maxwell's equations in a three-dimensional domain. The fully unstructured spatial discretization is made possible by the use of a high-order nodal basis, employing multivariate Lagrange polynomials defined on the triangles and tetrahedra, while the equations themselves are satisfied in a discontinuous Galerkin form with the boundary conditions being enforced weakly through a penalty term. Accuracy, stability, and convergence of the semidiscrete approximation to Maxwell's equations is established rigorously and bounds on the growth of the global divergence error are provided. Concerns related to efficient implementations are discussed in detail. This sets the stage for the presentation of examples, verifying the theoretical results, and illustrating the versatility, flexibility, and robustness when solving two- and three-dimensional benchmark problems in computational electromagnetics. Pure scattering as well as penetration is discussed and high parallel performance of the scheme is demonstrated.
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