@Article{IJNAM-2-15,
author = {Cao , Jianwen and Sun , Jiachang},
title = {An Efficient and Effective Nonlinear Solver in a Parallel Software for Large Scale Petroleum Reservoir Simulation},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2005},
volume = {2},
number = {0},
pages = {15--27},
abstract = {<p style="text-align: justify;">We study a parallel Newton-Krylov-Schwarz (NKS) based
algorithm for solving large sparse systems resulting from a fully
implicit discretization of partial differential equations arising from
petroleum reservoir simulations. Our NKS algorithm is designed by
combining an inexact Newton method with a rank-2 updated quasi-Newton
method. In order to improve the computational efficiency, both DDM and
SPMD parallelism strategies are adopted. The effectiveness of the
overall algorithm depends heavily on the performance of the linear
preconditioner, which is made of a combination of several
preconditioning components including AMC, relaxed ILU, up scaling,
additive Schwarz, CRP-like (constraint residual preconditioning), Watts
correction, Shur complement, among others. In the construction of the
CRP-like preconditioner, a restarted CMRES is used to solve the
projected linear systems. We have tested this algorithm and related
parallel software using data from some real applications, and presented
numerical results that show that this solver is robust and scalable for
large scale calculations in petroleum reservoir simulations.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/944.html}
}