Investigating iterative solvers of Poisson-type equations discretized by the Two-Point Flux-Approximation scheme

Abstract

I denne masteroppgaven ser vi på alternative iterative løsere til MATLABs innebygde direkte løser \texttt{mldivide} for Poisson-type problemer. Løserene er testet på to forskjellige modeller som er vanlig å bruke for optimeringstester: Olympus og SPE10. Det viser seg at de iterative løserene generelt er bedre enn \texttt{mldivide}, for store systemer. Det er klart at bruk av algebraisk multigrid (AMG) som prekondisjoner forbedrer konvergensen drastisk. Blandt de testede iterative løserene var det Krylov-løsere BiCGstab og BiCGstab($l$) kombinert med glatteren ILU(0) og forgrovningen "smoothed aggregation" som gjorde det best.

In this thesis we investigate alternative iterative solvers to MATLAB's in-built direct solver \texttt{mldivide} for Poisson-type problems. The solvers are tested on two models used for the purpose of benchmark studies for field development optimization: Olympus and SPE10. It is found that the iterative solvers, in general, perform better than \texttt{mldivide} for large, computationaly heavy systems. It is evident that the use of algebraic multigrid (AMG) as a preconditioner improves convergence dramatically. Among the tested iterative solvers it is Krylov solvers BiCGstab and BiCGstab($l$) combined with the smoother ILU(0) and the coarsening strategy smoothed aggregation that performed overall best.