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000021133 084__ $$2WoS$$aMathematics, Applied
000021133 1001_ $$0P:(DE-HGF)0$$aBolten, M.$$b0
000021133 245__ $$aPreconditioning systems arising from the KKR Green function method using block-circulant matrices
000021133 260__ $$aNew York, NY$$bAmerican Elsevier Publ.$$c2012
000021133 300__ $$a436 - 446
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000021133 440_0 $$024983$$aLinear Algebra and its Applications$$v436$$y2
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000021133 520__ $$aRecently, a linearly scaling method for the calculation of the electronic structure based on the Korringa-Kohn-Rostoker Green function method has been proposed. The method uses the transpose free quasi minimal residual method (TFQMR) to solve linear systems with multiple right hand sides. These linear systems depend on the energy-level under consideration and the convergence rate deteriorates for some of these energy points. While traditional preconditioners like ILU are fairly useful for the problem, the computation of the preconditioner itself is often relatively hard to parallelize. To overcome these difficulties, we develop a new preconditioner that exploits the strong structure of the underlying systems. The resulting preconditioner is block-circulant and thus easy to compute, invert and parallelize. The resulting method yields a dramatic speedup of the computation compared to the unpreconditioned solver, especially for critical energy levels. (C) 2011 Elsevier Inc. All rights reserved.
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000021133 65320 $$2Author$$aPreconditioning
000021133 65320 $$2Author$$aElectronic structure calculation
000021133 65320 $$2Author$$aBlock-circulant matrices
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