Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Domain decomposition algorithms with small overlap
SIAM Journal on Scientific Computing
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization
SIAM Journal on Numerical Analysis
Overlapping Schwarz methods for unstructured spectral elements
Journal of Computational Physics
Spectral methods for hyperbolic problems
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
Journal of Computational Physics
Approximation of acoustic waves by explicit Newmark's schemes and spectral element methods
Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
Journal of Computational Physics
Journal of Computational and Applied Mathematics
Journal of Computational Physics
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The classical overlapping Schwarz algorithm is here extended to the spectral element discretization of linear elastic problems, for both homogeneous and heterogeneous compressible materials. The algorithm solves iteratively the resulting preconditioned system of linear equations by the conjugate gradient or GMRES methods. The overlapping Schwarz preconditioned technique is then applied to the numerical approximation of elastic waves with spectral elements methods in space and implicit Newmark time advancing schemes. The results of several numerical experiments, for both elastostatic and elastodynamic problems, show that the convergence rate of the proposed preconditioning algorithm is independent of the number of spectral elements (scalability), is independent of the spectral degree in case of generous overlap, otherwise it depends inversely on the overlap size. Some results on the convergence properties of the spectral element approximation combined with Newmark schemes for elastic waves are also presented.