An element-by-element preconditioned conjugate gradient method implemented on a vector computer

Authors:
Jocelyne Erhel;Alice Traynard;Marina Vidrascu
Affiliations:
IRISA campus universitaire de Beaulieu, F-35042 Rennes Cedex, France;INRIA Rocquencourt B.P. 105, F-78153 Le Chesnay Cedex, France;INRIA Rocquencourt B.P. 105, F-78153 Le Chesnay Cedex, France
Venue:
Parallel Computing
Year:
1991

Citing 2
Cited 1

A preconditioning technique based on element matrix factorizations

Computer Methods in Applied Mechanics and Engineering
Large-scale vectorized implicit calculations in solid mechanics on a Cray X-MP/48 utilizing EBE preconditioned conjugate gradients

Computer Methods in Applied Mechanics and Engineering

A distributed memory parallel element-by-element scheme based on Jacobi-conditioned conjugate gradient for 3D finite element analysis

Finite Elements in Analysis and Design

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Abstract

We consider the linear equation Ax = b where A is a sparse symmetric positive definite matrix arising from a finite element discretisation. We use the preconditioned conjugate gradient method to solve this equation, introducing an element-by-element preconditioner which is based on a Crout's decomposition of the element matrices and an element-by-element product of them. When the mesh is coloured, this preconditioner is largely vectorizable. We implement this method on a CRAY-2, and test it on 2D and 3D elastic and thermal problems and compare it to other classical preconditioners.