Parallel application of a novel domain decomposition preconditioner for the adaptive finite-element solution of three-dimensional convection-dominated PDEs

Parallel Application of a Novel Domain Decomposition Preconditioner for the Stable Finite Element Solution of Three-Dimensional Convection-Dominated PDEs

Parallel scalability study of three dimensional additive Schwarz preconditioners in non-overlapping domain decomposition

In this paper we study the parallel scalability of variants of additive Schwarz preconditioners for three dimensional non-overlapping domain decomposition methods. To alleviate the computational cost, both in terms of memory and floating-point complexity, we investigate variants based on a sparse approximation or on mixed 32and 64-bit calculation. The robustness of the preconditioners is illust...

Communication-aware adaptive parareal with application to a nonlinear hyperbolic system of partial differential equations

In the strong scaling limit, the performance of conventional spatial domain decomposition techniques for the parallel solution of PDEs saturates. When sub-domains become small, halo-communication and other overheard come to dominate. A potential path beyond this scaling limit is to introduce domain-decomposition in time, with one such popular approach being the Parareal algorithm which has rece...

A Model for Parallel Adaptive Finite Element Software

The paper presents a conceptual model and details of an implementation for parallel adaptive finite element systems, particularly their computational kernels. The whole methodology is based on domain decomposition while message passing is used as a model of programming. The proposed finite element architecture consist of independent modules, most of them taken from sequential codes. The sequent...

Finite Element Methods for Convection Diffusion Equation

This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...