Tridiagonal Factorization Algorithm : A Preconditioner for Nonsymmetric System Solving on Vectorcomputers

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The Tridiagonal Factorization (TF) algorithm was originally introduced by the authors as a matrix splitting type preconditioner for regular sparse nonsymmetric system solving on vector and / or parallel computers. It has been re-introduced using a Preconditioner Introduction Process which also gives an alternative introduction process to the ILU preconditioner. The approximation properties of the TF and ILU preconditioners against the coefficient matrix of linear systems have been analyzed. It is shown that they have similar approximation properties versus the change in diffusion anisotropy as well as advection intensity of an advection diffusion equation. Convergence and CPU-time of both preconditioners have been compared for some practical 2D and 3D device simulation problems on the NEC SX-2 supercomputers. It is observed that the iterative procedures with the TF preconditioner are up to 3 times faster than those with vectorized ILU preconditioners.

The Tridiagonal Factorization (TF) algorithm was originally introduced by the authors as a matrix splitting type preconditioner for regular sparse nonsymmetric system solving on vector and / or parallel computers. It has been re-introduced using a Preconditioner Introduction Process, which also gives an alternative introduction process to the ILU preconditioner. The approximation properties of the TF and ILU preconditioners against the coefficient matrix of linear systems have been analyzed. It is shown that they have similar approximation properties versus the change in diffusion anisotropy as well as advection intensity of an advection diffusion equation. Convergence and CPU-time of both preconditioners have been compared for some practical 2D and 3D device simulation problems on the NEC SX-2 supercomputers. It is observed that the iterative procedures with the TF preconditioner are up to 3 times faster than those with vectorized ILU preconditioners.

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