Improvement of Block IC Preconditioner Using Fill-In Technique for Linear Systems Derived From Finite-Element Method Including Thin Elements

The block incomplete-Cholesky (IC) preconditioner is often used for parallel preconditioner in finite-element method (FEM) supported by distributed computing. When many thin elements are included in an analyzed mesh such as magnetic shielding, the convergence characteristic of preconditioned conjugate gradient method would be deteriorated. At that time, IC preconditioner with fill-in makes the convergence characteristic of linear solver much better. This paper demonstrates the validity of block IC with fill-in on linear systems arising in FEM with many flat elements. First, the ability to improve the convergence property using the fill-in strategy is verified by the simulation of magnetic shielding. Next, the parallelization performance of block IC with fill-in is illustrated by using finite-element mesh of laminated core model and induction heating cooker.