Coupling parallel asynchronous multisplitting methods with Krylov methods to solve pseudo-linear evolution 3D problems

The present study deals with pseudo-linear problems solving using parallel asynchronous multisplitting methods combined with Krylov methods. With appropriate and realistic assumptions, the behavior of such parallel iterative algorithms will be analyzed by partial ordering techniques in relation with the discrete maximum principle. Applications to discretized boundary value problems are presented, the implementation of the algorithms is described and parallel experiments are analyzed. •Solution of pseudo-linear problems evolution 3D problems using parallel asynchronous multisplitting methods combined with Krylov methods are used.•Behavior by partial ordering technique of the numerical parallel iterative algorithms is analyzed.•Two distinct application are presented and solved by the studied method.•Implementation of algorithms is described.•Numerical synchronous and asynchronous parallel simulation achieved on a grid are presented and compared.