High Order Methods for Shock Calculations and Computational Electromagnetics

本文的研究目标是研究冲击波计算和计算电磁学的高阶数值方法，高阶方法可以用较粗的网格来解决复杂的物理问题，从而减少计算量。 然而，高阶方法的冲击计算和计算电磁学涉及许多理论和实际问题，必须加以研究。 本文的工作涉及高阶有限差分、有限元和谱方法在计算流体力学和计算电磁学中的发展、分析和应用，重点是复杂几何和高效并行实现。特别是，该建议包含以下组成部分：高阶方法的冲击波计算，包括有限差分ENO和韦诺计划，有限元间断Galerkin方法，频谱方法，和高阶方法的计算电磁学，包括频谱方法，频谱multidomainmethods，和吸收层。预计所提出的努力将提高先进的高阶方法的不连续问题和长时间的积分，特别是在复杂的几何形状。

The objective of the proposed research is to study high order numericalmethods for shock calculations and for computational electromagnetics.High order methods can resolve complicated physical problems with arelatively coarse mesh, hence reducing computational cost for suchproblems. However, high order methods for shock calculations and forcomputational electromagnetics involve many theoretical and practicalissues which must be investigated. The proposed work involves thedevelopment, analysis, and applications of high order finite difference,finite element and spectral methods in the applications areas ofcomputational fluid dynamics and computational electromagnetics.Two emphasized aspects of the proposed effort are complex geometriesand efficient parallel implementations. In particular, the proposal contains the following components: high order methods for shock wave calculations, including finite difference ENO and WENO schemes, finite element discontinuous Galerkin methods, spectral methods, and high order methods in computationalelectromagnetics, including spectral methods, spectral multidomainmethods, and absorbing layers. It is expected that the proposed effort will improve the state of art in high order methods for discontinuous problems and long time integrations, especially in complex geometry.