We present a spectral-element discontinuous Galerkin lattice Boltzmann method for solving single-phase incompressible flows. Decoupling the collision step from the streaming step offers numerical stability at high Reynolds numbers. In the streaming step, we employ high-order spectral-element discretizations using a tensor product basis of one-dimensional Lagrange interpolation polynomials based...

We develop an efficient spectral-element method for computing the transmission eigenvalues in two-dimensional radially stratified media. Our method is based on a dimension reduction approach which reduces the problem to a sequence of one-dimensional eigenvalue problems that can be efficiently solved by a spectral-element method. We provide an error analysis which shows that the convergence rate...

The propagation of seismic waves through Earth can now be modeled accurately with the recently developed spectral-element method. This method takes into account heterogeneity in Earth models, such as three-dimensional variations of seismic wave velocity, density, and crustal thickness. The method is implemented on relatively inexpensive clusters of personal computers, so-called Beowulf machines...

The Nonconforming Spectral Element Method (NSEM) solves PDEs in complex geometries with high accuracy, however, it is an expensive method. Since parallel computation is eeective in decreasing CPU time, a parallel algorithm for the NSEM is presented. Implementations on SGI Power Challenge using MPI are evaluated in terms of measured speedup and parallel eeciency for schemes of one element and mu...

We employ a two-dimensional spectral element method to investigate the effect of various semi-circular blockages on the laminar flow between two flat plates. This simplified geometry has a general relevance to blocked flows, but more academically, also relates to work on the backward-facing step, presenting a qualitatively similar flow with a single, independent step, or blockage, parameter. Th...

This paper investigates the vibration bandgap properties of two-dimensional (2D) periodic composite beam frame structures with component defects. Combined topological characteristics structure, a generalized position coordinate system is proposed, and an assembly method stiffness matrix for virtual full model presented. Then spectral equations motion whole 2D ones defects are established. Compa...

The thesis aims to solve partial differential equations numerically using mimetic spectral element method. The method rewrites the PDEs with differential forms so the resulting equations are able to preserve geometrical characteristics in physics. The equation we focus is the Poisson equation, which can be utilized for potential flow problems. The physical domain to be tested is a typical flow ...

We provide a detailed presentation and discussion of a numerical modeling technique for earthquake dynamics based on the spectral element method. The problem of dynamic frictional contact along slip interfaces in elastic domains is formulated in a hybrid variational form, with Lagrange multipliers associated to the fault tractions. The problem is discretized in space by a spectral element metho...

Magnesium is an abundant element in the environment. Magnesium ion sensing by fluorescence spectral method is of importance due to the need for the detection of the metal in the human body and the environment. In this paper, we report the Mg2+ ion sensing behavior of the phenylhydrazone derivative of a difluorenylpiperidin-4-one. The preparation method of this compound is simple. The compound s...