An indefinite overlapping Schwarz method is introduced and studied for Stokes problems discretized with Qn−Qn−2 spectral elements. This results in a parallel and scalable preconditioner for the iterative solution of the discrete system of equations. The preconditioner is based on the solution of local Stokes problems on overlapping subregions and a coarse Stokes problem with Q2−Q0 elements. The efficiency of the method is based on using a nodal basis and quadrature rules associated with Gauss–Lobatto–Legendre nodes. As for h-version finite elements, a small overlap between subregions seems to be the most efficient choice.
Domain decomposition methods with small overlap for Qn−Qn−2 spectral elements / L.F. Pavarino. - In: APPLIED NUMERICAL MATHEMATICS. - ISSN 0168-9274. - 33:1-4(2000), pp. 463-470.
Domain decomposition methods with small overlap for Qn−Qn−2 spectral elements
L.F. PavarinoPrimo
2000
Abstract
An indefinite overlapping Schwarz method is introduced and studied for Stokes problems discretized with Qn−Qn−2 spectral elements. This results in a parallel and scalable preconditioner for the iterative solution of the discrete system of equations. The preconditioner is based on the solution of local Stokes problems on overlapping subregions and a coarse Stokes problem with Q2−Q0 elements. The efficiency of the method is based on using a nodal basis and quadrature rules associated with Gauss–Lobatto–Legendre nodes. As for h-version finite elements, a small overlap between subregions seems to be the most efficient choice.Pubblicazioni consigliate
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