A COMPARATIVE STUDY OF GLOBAL AND LOCAL PRECONDITIONERS FOR PARALLEL FINITE ELEMENT COMPUTATIONS

Resumo

Numerous engineering problems require an enormous computational effort to solve large
sparse linear systems with matrices resulting of finite element discretizations. Parallel computing of
GMRES or other Krylov subspace-based method combined with a good preconditioner is an excellent
option to fulfill this role. Mostelly, the two main operations of Krylov subspace methods, the inner
and the matrix-vector products, demand less memory consumption and present better parallelism when
compared with the main operations of the traditional direct solvers. Global storage allows the use of
block Jacobi preconditioners based on incomplete LU factorization. In contrast, local storage schemes

provide preconditioners performed at the element level factorizations (e.g., the local LU, the local Gauss-
Seidel and the diagonal or the block-diagonal schemes). In this work, we present a trade-off analysis

between global and local preconditioners for parallel finite element implementations. In the context of a
specific domain decomposition approach, we evaluate the preconditioners according to memory usage,
load balancing and MPI communication. Robustness and scalability of these parallel preconditioning
strategies are demonstrated for two benchmark cases: the rotating cone modeled by the transient transport
equation, and the explosion problem modeled by the Euler equations. All experiments point out the
supremacy of the global preconditioners, and the local preconditioners dependence on the number of
degrees of freedom per node.