Journal of Computational Physics
A second-order accurate pressure correction scheme for viscous incompressible flow
SIAM Journal on Scientific and Statistical Computing
The construction of preconditioners for elliptic problems by substructuring. I
Mathematics of Computation
Schur complement domain decomposition algorithms for spectral methods
Applied Numerical Mathematics - Spectral multi-domain methods
SIAM Journal on Scientific and Statistical Computing - Special issue on iterative methods in numerical linear algebra
Direct numerical simulation of transition and turbulence in a spatially evolving boundary layer
Journal of Computational Physics
Efficient variants of the vertex space domain decomposition algorithm
SIAM Journal on Scientific Computing
Journal of Computational Physics
Unstructured spectral element methods for simulation of turbulent flows
Journal of Computational Physics
SIAM Journal on Numerical Analysis
On error estimates of the projection methods for the Navier-Stokes equations: second-order schemes
Mathematics of Computation
Timely Communication: Diagonal Edge Preconditioners in p-version and Spectral Element Methods
SIAM Journal on Scientific Computing
The Spectral Projection Decomposition Method for Elliptic Equations in Two Dimensions
SIAM Journal on Numerical Analysis
A spectral multidomain method for the numerical simulation of turbulent flows
Journal of Computational Physics
Quasi-Optimal Schwarz Methods for the Conforming Spectral Element Discretization
SIAM Journal on Numerical Analysis
Terascale spectral element algorithms and implementations
SC '99 Proceedings of the 1999 ACM/IEEE conference on Supercomputing
Overlapping Schwarz methods for unstructured spectral elements
Journal of Computational Physics
Fast parallel direct solvers for Coarse Grid problems
Journal of Parallel and Distributed Computing
Algebraic Two-Level Preconditioners for the Schur Complement Method
SIAM Journal on Scientific Computing
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Hi-index | 31.45 |
In this paper we present a preconditioned multi-domain algorithm applied to the elliptic kernels arising from the spectral collocation of the incompressible Navier Stokes equations in three space dimensions with one homogeneous direction. The technique, based on the iterative solution of the Schur complement matrix, allows for efficient numerical solution of the operators in complex geometries consisting of a collection of non-overlapping rectangular subdomains. The method is shown to be nearly optimal in terms of condition number behavior in a double path of refinement strategy, i.e. whenever both the number of Legendre modes and the number of subdomains are significantly increased. It is thus well suited for engineering applications in the fields of direct numerical simulation and large eddy simulation of turbulence.