JPSOL(J Parallel Solver Library for Numerical Algebra Problems) is introduced, including the software architecture, matrix vector data structure, three kinds of algorithm libraries (linear, nonlinear and eigenvalue) and domain specific solvers. Then, the high parallel scalability of JPSOL are demonstrated by the testing results of basic iterative methods. Finally, the effect and robustness of JPSOL are demonstrated by several typical practical applications.

To address the high computational complexity of sparse linear solvers caused by complex physical characteristics in practical applications, this paper presents a unified framework for feature-modified preconditioning algorithms. By refining the algebraic features affecting the efficiency from physical characteristics and combining multilevel feature analysis, we construct feature-modified components. The effectiveness of this framework is demonstrated through several typical feature-modified preconditioning algorithms and their application results.

An algebraic multigrid (AMG) algorithm based on hybrid coarsening is proposed for the linear systems of the discrete pressure Poisson which is derived from the SIMPLE algorithm for the Navier-Stokes equations in complex flows. This algorithm combines a class of non-smoothed aggregation coarsening with classical C/F coarsening to construct grid hierarchy, hoping to reduce the cost in the setup phase of the AMG algorithm without affecting convergence. The high performance of the proposed algorithm is verified by numerical simulation of complex flow in the combustion chamber of aero-engine. The results show that the proposed algorithm can achieve 78% acceleration compared with the classical AMG algorithm.