Explicit approximate inverse finite element preconditioning for solving biharmonic equations

摘要

A new class of coupled equation approach in conjunction with approximate inverse finite element matrix techniques based on the concept of sparse approximate LU-type factorization procedures is introduced for solving biharmonic equations. Explicit preconditioned conjugate gradient - type schemes based on approximate inverse matrix techniques are presented for the efficient solution of finite element linear systems. Application of the proposed method on linear two and three dimensional biharmonic problems is discussed and numerical results are given.