More Levels Ilu Decomposition And The Application In The Electromagnetic Computing Research

The research of fast and effective methods for solving large sparse linear systemsis the focus of scientific computing, and it has important theoretic significance andpractical applications. This is because in many areas of practice such as computationalelectromagnetics, fluid dynamics, numerical weather prediction, materials simulationand design, seismic data processing, and oil exploration data processing all need to getthe numerical solution of differential equations. Through the finite element, finitedifference, domain decomposition, finite volume, non-grid and multigrid methods,differential equations can be discretized, and finally it can change to slove large-scalelinear equations.In this dissertation, we deeply study multi-level ILU preconditioning methods andimprove some preconditioners. This thesis consists of four parts.Brief introductions of the research background and significance of multi-level ILUpreconditioner methods are given.We briefly introduce some important Krylov subspace methods and analyze theproperty of some simple preconditioners.The article gives the simple multi-level ILU methods and in the constrution ofindependent set we offer a strategy of using the entire matrix‘s diagonally dominantproperty, namely, normalizing diagonally dominant weight. Studies have shown that thenormalized multi-level ILU method has more efficiently using the entire matrix‘sdiagonally dominant property.Base on the property of the triangular block preconditioner and the secondpreconditioner, we modify the triangular block preconditioner. Under the analysis of themodified triangular block preconditioner at different coefficients, we conclude that themodified triangular block preconditioner has better convergence property than originaltriangular block preconditioner when the system matrix is relatively dense.