Spectral element method for stability analysis of milling processes with discontinuous time-periodicity

A Discontinuous Spectral Element Method for the Level Set Equation

An Efficient High-Order Time Integration Method for Spectral-Element Discontinuous Galerkin Simulations in Electromagnetics

We investigate efficient algorithms and a practical implementation of an explicittype high-order timestepping method based on Krylov subspace approximations, for possible application to large-scale engineering problems in electromagnetics. We consider a semi-discrete form of the Maxwell’s equations resulting from a high-order spectral-element discontinuous Galerkin discretization in space whose...

Analysis of an hp-Nonconforming Discontinuous Galerkin Spectral Element Method for Wave Propagation

We analyze the consistency, stability, and convergence of an hp discontinuous Galerkin spectral element method of Kopriva [J. Comput. Phys., 128 (1996), pp. 475–488] and Kopriva, Woodruff, and Hussaini [Internat. J. Numer. Methods Engrg., 53 (2002), pp. 105–122]. The analysis is carried out simultaneously for acoustic, elastic, coupled elastic-acoustic, and electromagnetic wave propagation. Our...

Analysis of an Hp-Non-conforming Discontinuous Galerkin Spectral Element Method for Wave

We analyze the consistency, stability, and convergence of an hp discontinuous Galerkin spectral element method. The analysis is carried out simultaneously for acoustic, elastic, coupled elastic–acoustic, and electromagnetic wave propagation. Our analytical results are developed for both conforming and non-conforming approximations on hexahedral meshes using either exact integration with Legendr...

Time-Discontinuous Finite Element Analysis of Two-Dimensional Elastodynamic Problems using Complex Fourier Shape Functions

This paper reformulates a time-discontinuous finite element method (TD-FEM) based on a new class of shape functions, called complex Fourier hereafter, for solving two-dimensional elastodynamic problems. These shape functions, which are derived from their corresponding radial basis functions, have some advantages such as the satisfaction of exponential and trigonometric function fields in comple...