Abstract
A new variant of Incomplete Factorization Implicit (IFI) iterative technique for 2D elliptic finite-difference (FD) equations is suggested which is differed by applying the matrix tridiagonal algorithm. Its iteration parameter is shown be linked with the one for Alternating Direction Implicit method. An effective set of values for the parameter is suggested. A procedure for enhancing the set of iteration parameters for IFI is proposed. The technique is applied to a 5-point FD scheme, and to a 9-point FD scheme. It is suggested applying the solver for 5-point scheme to solving boundary-value problems for the 9-point scheme, too. The results of numerical experiment with Dirichlet and Neumann boundary-value problems for Poisson equation in a rectangle, and in a quasi-circle are presented. Mixed boundary-value problems in square are considered, too. The effectiveness of IFI is high, and weakly depends on the type of boundary conditions.
Highlights
The Incomplete Factorization iterative method (IF) for solving 2D and 3D elliptic finite-difference (FD) equations was suggested by Buleev [2]
Sabinin [8,10] observed a similarity of iteration parameters for Incomplete Factorization Implicit (IFI) and ones for Alternating Direction Implicit (ADI) method, and he proposed a cyclic set of parameters which permitted the effective solving boundary-value problems
Following [15], the set of ADI parameters by Jordan [16] gives for IFI the cyclical set of increasing values ω (S is the period of cycle): ωs = 1 − 2Ωs, s = 0, ..., S − 1 ; ωs = ωs−S, s ≥ S, (3.3)
Summary
The Incomplete Factorization iterative method (IF) for solving 2D and 3D elliptic finite-difference (FD) equations was suggested by Buleev [2]. Sabinin [8,10] observed a similarity of iteration parameters for IFI and ones for Alternating Direction Implicit (ADI) method, and he proposed a cyclic set of parameters which permitted the effective solving boundary-value problems. New variant of IFI technique is suggested which is different by applying the matrix algorithm of Thomas for enhancing stability This is applied to as 5-point, as to high-order 9-point FD schemes of type ”cross” for 2D elliptic problems. It is suggested for IFI the cyclic set of iteration parameters, and the ”hammer” sequence of parameters inside the cycle.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
