it is well-known that dam-reservoir interaction has significant effects on the response of dams to the earthquakes. this phenomenon should be considered more exactly in the seismic design of dams with a rational and reliable dynamic analysis method. in this research, seismic analysis of the dam-reservoir is studied as a wave propagation problem by using legendre spectral element method (sem). t...

Spectral element methods (SEM) are superior to general finite element methods (FEM) in achieving high order accuracy through p-type refinement. Owing to orthogonal polynomials in both expansion and test functions, the discretization errors in SEM could be reduced exponentially to machine zero so that the spectral convergence rate can be achieved. Inherited the advantage of FEM, SEM can enhance ...

The spectral element method (SEM) is a high order numerical method for solving partial differential equations that inherits the accuracy of spectral methods and the geometrical flexibility of the finite element method. These lectures provide an introduction to the SEM for graduate students in Earth science. The construction of the method is described for a model problem in 1D and 2D. The elemen...

In this note is presented a method, given nodal values on multidimensional nonconforming spectral elements, for calculating global Fourier-series coefficients. This method is “exact” in that given the approximation inherent in the spectral-element method (SEM), no further approximation is introduced that exceeds computer round-off error. The method is very useful when the SEM has yielded an ada...

Summary: Spectral element methods (SEM) exhibit exponential convergence only when the solution of the problem is sufficiently regular. However, the solution develops a singularity when the boundary of the domain is non-smooth. The accuracy of the SEM is then deteriorated and they offer no advantage over low order methods. Such problems frequently occur in many important physical applications, f...

In this paper, we compare a triangle based spectral element method (SEM) with the classical quadrangle based SEM and with a standard spectral method. For the sake of completeness, the triangle-SEM, making use of the Fekete points of the triangle, is first revisited. The requirement of a highly accurate quadrature rule is particularly emphasized. Then it is shown that the convergence properties ...

A three-dimensional spectral element method SEM was developed for analysis of Lamb wave propagation in composite laminates containing a delamination. SEM is more efficient in simulating wave propagation in structures than conventional finite element method FEM because of its unique diagonal form of the mass matrix. Three types of composite laminates, namely, unidirectional-ply laminates, cross-...

This paper presents the large-eddy simulation of the lid-driven cubic cavity flow by the spectral element method (SEM) using the dynamic model. Two spectral filtering techniques suitable for these simulations have been implemented. Numerical results for Reynolds number Re = 12000 are showing very good agreement with other experimental and DNS results found in the literature.