A comparative study of local and global preconditioners for finite element analysis
Laisa Karoline Muller1; Leonardo Muniz de Lima1; Lucia Catabriga1
1 Federal University of Espírito Santo
doi:10.20906/CPS/CILAMCE2017-0937
Resumo
Finite element method (FEM) invariably leads to solving large and sparse linear systems of equations. Excellent options include nonstationary iterative Krylov methods such as Generalized Minimal Residual (GMRES). Krylov methods demand matrix-vector products as one of the main operation, which efficiency depends on matrix storage. In addition, non-symmetric linear systems from convective dominant problems have slow convergence requiring suitable preconditioners. An efficient storage format is important in order to obtain low memory usage and high computational performance. The resulting matrices from finite element analysis can be stored locally using element by element (EBE) data strategy or globally using Compressed Storage Row (CSR) format. Global storage allows us to use effective preconditioners like incomplete LU factorization (ILU) combined with matrix reordering schemes while local storage schemes provide simple and efficient implementations of diagonal block based preconditioners. In this work we present a relevant trade-off analysis between local and global preconditioners for finite element implementations performing many examples considering advective-diffusive-reactive and inviscid compressible flows.
Palavras-chave: Finite element method; GMRES method; Global preconditioners; Local preconditioners