Solver preconditioning using the combinatorial multilevel method on reservoir simulation

摘要: The purpose of this paper is to report the first preliminary study recently introduced combinatorial multilevel (CML) method for solver preconditioning in large-scale reservoir simulation with coupled geomechanics. CML a variant popular algebraic multigrid (AMG) yet essential differences. basic idea new approach construct hierarchy matrices using discrete geometry graph, based on support theory preconditioners. In way, combines merits both geometric and methods. resulting hybrid not only provides simpler faster setup phase compared AMG, but can be proven exhibit strong convergence guarantees arbitrary symmetric diagonally dominant matrices. addition, underlying theoretical soundness contrasts heuristic AMG approach, which often show slow difficult problems. This implemented simulator pressure poroelastic displacement preconditioners multistage technique. We present results several known benchmark problems provide comparison performance complexity widespread schemes used simulation. An adaptation non-symmetric shown excellent properties realistic cases.