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
Journal of Computational Physics
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
A Reduced-Basis Element Method
Journal of Scientific Computing
Overlapping Schwarz and Spectral Element Methods for Linear Elasticity and Elastic Waves
Journal of Scientific Computing
Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics (Scientific Computation)
Overlapping Schwarz Methods for Fekete and Gauss-Lobatto Spectral Elements
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Hi-index | 7.29 |
Overlapping Schwarz preconditioners are constructed and numerically studied for Gauss-Lobatto-Legendre (GLL) spectral element discretizations of heterogeneous elliptic problems on nonstandard domains defined by Gordon-Hall transfinite mappings. The results of several test problems in the plane show that the proposed preconditioners retain the good convergence properties of overlapping Schwarz preconditioners for standard affine GLL spectral elements, i.e. their convergence rate is independent of the number of subdomains, of the spectral degree in the case of generous overlap and of the discontinuity jumps in the coefficients of the elliptic operator, while in the case of small overlap, the convergence rate depends on the inverse of the overlap size.