Local preconditioners for two‐level non‐overlapping domain decomposition methods

Abstract

We consider additive two-level preconditioners, with a local and a global component, for the Schur complement system arising in non-overlapping domain decomposition methods. We propose two new parallelizable local preconditioners. The ÿrst one is a computationally cheap but numerically relevant alternative to the classical block Jacobi preconditioner. The second one exploits all the information from the local Schur complement matrices and demonstrates an attractive numerical behaviour on heterogeneous and anisotropic problems. We also propose two implementations based on approximate Schur complement matrices that are cheaper alternatives to construct the given preconditioners but that preserve their good numerical behaviour. Through extensive computational experiments we study the numerical scalability and the robustness of the proposed preconditioners and compare their numerical performance with well-known robust preconditioners such as BPS and the balancing Neumann-Neumann method. Finally, we describe a parallel implementation on distributed memory computers of some of the proposed techniques and report parallel performances.

Iterative versus direct parallel substructuring methods in semiconductor device modelling

“…In this case [17], we try to exploit all the information available on each subdomain and we associate each subspace U i with the entire boundary i of subdomain i . Here, we have R i ≡ R i .…”

“…The preconditioners presented in this section were originally proposed in Reference [17]. In order to describe these preconditioners, we need ÿrst to deÿne a partition of B, the set of edges of the discretization belonging to the interface between the subdomains.…”

Avanços em Métodos de Krylov para Solução de Sistemas Lineares de Grande Porte

“…De forma completamente algébrica pode-se calcular a matriz do complemento de Schur das incógnitas da interface em relação às demais incógnitas. O problema é resolvido para a interface e a solução serve de condição de fronteira para os problemas internos que podem ser resolvidos de forma independente [28], [29] e [30]. Esse métodos recebem várias denominações, entre elas métodos de subestruturação ou métodos do complemento de Schur.…”

Operator trigonometry of preconditioning, domain decomposition, sparse approximate inverses, successive overrelaxation, minimum residual schemes

“…This could be worked out elsewhere. Also the same considerations will apply for Schur complement domain decompositions, such as those in Reference [32].…”