In this paper, the spectral element (SE) method is applied in time to find the entire time-periodic or transient solution of time-dependent differential equations. The time-periodic solution is computed by enforcing periodicity of the element set. Of particular interest are periodic forcing functions possessing high frequency content. To maintain the spectral accuracy for such forcing functions...

In this paper, flow past around two circular cylinders which are tandem arranged at a Reynolds number of 200 is numerically investigated by spectral element method. To validate the numerical method for incompressible Navier–Stokes equations, the benchmark problem of flow over a single circular cylinder is employed, with the numerical results in a good agreement with the available literatures. T...

The traveltimes of underside shear wave reflections (i.e. SS precursors) are widely used data for mapping the topography of mantle discontinuities in the upper mantle. Here, we examine the accuracy of ray theory in estimating the contribution of shear velocity heterogeneity in the mantle to SS–S400S, SS–S670S and S400S–S670S traveltimes. We analyse stacks of spectral-element method waveforms co...

This paper describes a novel numerical model aiming at solving moving-boundary problems such as free-surface flows or fluid-structure interaction. This model uses a moving-grid technique to solve the Navier–Stokes equations expressed in the arbitrary Lagrangian-Eulerian kinematics. The discretization in space is based on the spectral element method. The coupling of the fluid equations and the m...

Electrical and Computer Engineering) A Hybrid Spectral-Element / Finite-Element Time-Domain Method for Multiscale Electromagnetic Simulations by Jiefu Chen Department of Electrical and Computer Engineering Duke University

A high-order, conservative, yet efficient method named the spectral volume (SV) method is developed for conservation laws on unstructured grids. The concept of a “spectral volume” is introduced to achieve high-order accuracy in an efficient manner similar to spectral element and multidomain spectral methods. Each spectral volume is further subdivided into control volumes, and cell-averaged data...

‎In this paper‎, ‎we study spectral element approximation for a constrained‎ ‎optimal control problem in one dimension‎. ‎The equivalent a posteriori error estimators are derived for‎ ‎the control‎, ‎the state and the adjoint state approximation‎. ‎Such estimators can be used to‎ ‎construct adaptive spectral elements for the control problems.

The Community Atmosphere Model (CAM) version 5 includes a spectral element dynamical core option from NCAR’s High-Order Method Modeling Environment. It is a continuous Galerkin spectral finite element method designed for fully unstructured quadrilateral meshes. The current configurations in CAM are based on the cubedsphere grid. The main motivation for including a spectral element dynamical cor...

Algebraic multigrid is investigated as a solver for linear systems that arise from high-order spectral element discretizations. An algorithm is introduced that utilizes the efficiency of low-order finite elements to precondition the high-order method in a multilevel setting. In particular, the efficacy of this approach is highlighted on simplexes in two and three dimensions with nodal spectral ...

We present constructive a priori error estimates forH 0 -projection into a space of polynomials on a one-dimensional interval. Here, “constructive” indicates that we can obtain the error bounds in which all constants are explicitly given or are represented in a numerically computable form. Using the properties of Legendre polynomials, we consider a method by which to determine these constants t...