A robust ILU preconditioner using constraints diagonal Markowitz

In science and engineering, modeling and simulations are popularly used to gather knowledge and explain a complicated phenomena. These models are typically represented in partial differential equations (PDEs) which can be solved using meshes and sparse matrices. The solution cost of PDEs are dominated by the solution cost of sparse linear systems. Therefore, an efficient sparse linear solver becomes more important with the popularity of scientific modeling and simulations. In this paper, we proposed a robust incomplete LU preconditioning algorithm using constraints diagonal Markowitz. Experimental results with various linear systems show that ILU algorithm using constraints diagonal Markowitz shows better performance and more stable than traditional ILU algorithm with predefined ordering.