We study the performance of the multigrid method applied to spectral element (SE) discretizations of the Poisson and Helmholtz equations. Smoothers based on finite element (FE) discretizations, overlapping Schwarz methods, and point-Jacobi are considered in conjunction with conjugate gradient and GMRES acceleration techniques. It is found that Schwarz methods based on restrictions of the origin...

To investigate the nature of Pn propagation, we have implemented the spectral-element method (SEM) for vertically and laterally varying media with and without attenuation. As a practical measure, essential features of the Pn waves are distilled into seismic attributes including arrival times, amplitudes and pulse frequencies. To validate the SEM simulations, we first compare the SEM results wit...

It is well known that the spectral solutions of conservation laws have the attractive distinguishing property of infiniteorder convergence (also called spectral accuracy) when they are smooth (e.g., [C. Canuto, M.Y. Hussaini, A. Quarteroni, T.A. Zang, Spectral Methods for Fluid Dynamics, Springer-Verlag, Heidelberg, 1988; J.P. Boyd, Chebyshev and Fourier Spectral Methods, second ed., Dover, New...

A spectral-element technique to approximate partial diierential equations on an innnite domain is examined. The method is based on Boyd's mapping of a semi-innnite interval to a nite interval, and it is extended to a variational setting which allows for an implementation using a spectral-element method. By extending the method to a variational form, a straightforward implementation allows for h...

Polynomial extensions play a vital role in the analysis of the p and h-p FEM and the spectral element method. We construct explicitly polynomial extensions on standard elements: cubes, triangular prisms and pyramids, which together with the extension on tetrahedrons are used by the p and h-p FEM in three dimensions. These extensions are proved to be stable and compatible with FEM subspaces on t...

Polynomial extensions play a vital role in analysis of the p and h-p FEM as well as spectral element method. In this paper, we construct explicitly polynomial extensions on a triangle T and a square S, which lift a polynomial defined on a side Γ or on whole boundary of T or S. The continuity of these extension operators from H 1 2 00(Γ) to H (T ) or H(S) and from H 1 2 (∂T ) to H(T ) or from H ...

Detecting damages in its early stage, and hence, to ensure the safety and reliability of structures is of vital important. Guided waves have been recognised as one of the promising damage detection techniques that are sensitive to small and different types of damages. The understanding of guided wave propagation and scattering phenomena at the damages is one of the fundamental elements to facil...

Certain results of numerical simulations obtained by the use of the spectral finite element method in time domain are presented by the authors. They were selected in order to show the effectiveness of the spectral finite element method for investigation of problems associated with propagation of guided elastic waves in a wind turbine laminated composite blade. Results of these simulations were ...

A least-squares spectral finite element method was used to develop an accurate computer code for prediction of solidification from a melt under the influence of an externally applied magnetic field. The computational results indicate significantly different flow-field patterns and thermal fields in the melt and the accrued solid in the cases of full gravity, reduced gravity, and an applied unif...

In this paper we show that we can use a modified version of the h-p spectral element method proposed in [6,7,13,14] to solve elliptic problems with general boundary conditions to exponential accuracy on polygonal domains using nonconform-ing spectral element functions. A geometrical mesh is used in a neighbourhood of the corners. With this mesh we seek a solution which minimizes the sum of a we...