Augmented conjugate gradient. Application in an iterative process for the solution of scattering problems |
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Authors: | MO Bristeau J Erhel |
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Institution: | (1) INRIA, B.P. 105, Rocquencourt, F-78153 Le Chesnay Cedex, France E-mail:;(2) INRIA, Campus Universitaire de Beaulieu, F-35042 Rennes Cedex, France |
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Abstract: | We discuss the application of an augmented conjugate gradient to the solution of a sequence of linear systems of the same
matrix appearing in an iterative process for the solution of scattering problems. The conjugate gradient method applied to
the first system generates a Krylov subspace, then for the following systems, a modified conjugate gradient is applied using
orthogonal projections on this subspace to compute an initial guess and modified descent directions leading to a better convergence.
The scattering problem is treated via an Exact Controllability formulation and a preconditioned conjugate gradient algorithm
is introduced. The set of linear systems to be solved are associated to this preconditioning. The efficiency of the method
is tested on different 3D acoustic problems.
This revised version was published online in August 2006 with corrections to the Cover Date. |
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Keywords: | conjugate gradient Krylov subspace least-squares scattering 65F10 65C20 |
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