Appreciation Of Incomplete Lu Decomposition And Its Applications

When researching practical problems of mathematics, partial differential equation isa kind of very important task. Solving method is discreting this equation, and get largesparse linear equations. solving large sparse linear equations is our main research topicand preconditioned iterative method is an effective way to solve such problems. In ourpresent methods of solving linear equations such as preconditioned GMRES,BI-CGSTAB, They are strong, and it is applicable In many cases. When Large sparselinear system discrete from partial differential equations and get numerical solution, themethod is also often used. Early iteration methods have Jacobi, Gauss-seidel etc..preconditioned methods are sparse approximate inverse, incomplete LU decomposition,sorting, etc. Incomplete LU decomposition is a highly versatile method. It make thematrices triangle decomposition through the complete LU, Then give up part of theelement, this paper mainly studies the ILU method.In many complex engineering fields such as in the electromagnetic field oftenoccurred of a class of elliptic equations-Helmholtz equations. When wave numberincreases, it will appear high concussion phenomenon. So it becomes a kind ofchallenges for solving this kind of equations. Better solving it is very significant for theelectromagnetic field numerical calculation. This paper discrete the2d Helmholtzequations by the finite difference method, and get large sparse linear system. To speedup the convergence speed, we use preconditioned technology to the large sparse linearsystems. In this paper,aiming at this kind of equations I come up with a kind of effectiveILU decomposition, First, we found the minimum F norm ofR LX2UFby the approximate inversion technology,X Uis the successive updating volume. In theinitial value selection, Objective function G getG L1R, and has successive iteration,finally solve by using iterative method. The original ILUT and the improved ILU arecompared; numerical tests show that this method is rising the convergence speed anditeration time.