Fast Linear Solvers

Hongsen Chen and Man-Chung Yeung



At first, some problems in the solution of linear systems in the reservoir simulator are introduced, such as the matrix structure spoiled by well perforation and unstructured grids, accurate direct solvers but slow, and preconditioned iterative solvers for large scale systems. Many linear solvers of CG, MINRES, GMERS, BICG, CGS, BiCGSTAB and ML(n)BiCGSTAB are illustrated in details. Number of Newton iterations for simulating a realistic black oil model with ML(1, 2, 3, 5, 9) BiCGSTAB and ML(n)BiCGSTAB respectively are compared. The percentage of improvement of ML(n)BiCGSTAB method over the BiCGSTAB method is also shown in the plotted figure.