Efficient Preconditioned Solution Methods for Elliptic Partial Differential Equations

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This e-book presents several research areas of elliptical problems solved by differential equations. The mathematical models explained in this e-book have been contributed by experts in the field and ...
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Efficient Preconditioners for Saddle Point Systems

Pp. 23-43 (21)

Zhi-Hao Cao

Abstract

Various block preconditioners for two by two block linear saddle point systems are studied. All block preconditioners are derived from a splitting of the (1,1) block of the two by two block matrix. We analyze the properties of the corresponding preconditioned matrices, in particular their spectra, and discuss the computational performance of the preconditioned iterative methods. It is shown that fast convergence depends mainly on the quality of the splitting of the (1,1) block. Moreover, some strategies of the implementation of the block preconditioners based on purely algebraic considerations are discussed. Thus, applying our block preconditioners to the related saddle point problems, we obtain preconditioned iterative methods in a “black box” fashion.

Keywords:

saddle point systems, iterative methods, preconditioning, convergence, algebraic, eigenvalues, block preconditioners

Affiliation:

School of Mathematical Sciences and Laboratory of Mathematics for Nonlinear Sciences, Fudan University, Shanghai, People's Republic of China.