Overlapping Schwarz Methods for Fekete and Gauss–Lobatto Spectral Elements

Overlapping Schwarz Methods for Fekete and Gauss-Lobatto Spectral Elements

The classical overlapping Schwarz algorithm is here extended to the triangular/tetrahedral spectral element (TSEM) discretization of elliptic problems. This discretization, based on Fekete nodes, is a generalization to nontensorial elements of the tensorial Gauss–Lobatto–Legendre quadrilateral spectral elements (QSEM). The overlapping Schwarz preconditioners are based on partitioning the domain...

Overlapping Schwarz Methods for Helmholtz's Equation

Overlapping Schwarz Preconditioners for Spectral Nédélec Elements for a Model Problem in H(curl)

A two-level overlapping domain decomposition method is analyzed for a Nédélec spectral element approximation of a model problem appearing in the solution of Maxwell’s equations. The overlap between subdomains can consist of entire spectral elements or rectangular subsets of spectral elements. For fixed relative overlap and overlap made from entire elements, the condition number of the method is...

Overlapping Schwarz Algorithms For

Overlapping Schwarz