Explicit Approximate Inverse Finite Element Preconditioning
For Solving Biharmonic Equations
Author(s)
G. A. Gravvanis
Abstract
Explicit approximate inverse finite element
preconditioning for solving biharmonic
equations
George A. Gravvanis
Department of Mathematics, University of the Aegean, Greece
Abstract
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.
1 Introduction
Let us consider a class of problems defined by the Partial Differential
Equation:
_4 _4 _4
4 d u d u d u /_. _,\ _ o—D (i V u(x,y) =-+ 2-+-=f(x,y), (x,
Keywords
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