This book deals with algorithms for the solution of linear systems of algebraic equations with large-scale sparse matrices, with a focus on problems that are obtained after discretization of partial differential equations using finite element methods. The authors provide a systematic presentation of the recent advances in robust algebraic multilevel methods and algorithms, e.g., the preconditioned conjugate gradient method, algebraic multilevel iteration (AMLI) preconditioners, the classical algebraic multigrid (AMG) method and its recent modifications, namely AMG using element interpolation (AMGe) and AMG based on smoothed aggregation. The first six chapters can serve as a short introductory course on the theory of AMLI methods and algorithms. The next part of the monograph is devoted to more advanced topics, including the description of new generation AMG methods, AMLI methods for discontinuous Galerkin systems, looking-free algorithms for coupled problems etc., ending with important practical issues of implementation and challenging applications. This second part is addressed to some more experienced students and practitioners and can be used to complete a more advanced course on robust AMLI and AMG methods and their efficient application. This book is intended for mathematicians, engineers, natural scientists etc.
Thisbook is the firstvolume of three volume series recording the""Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment"" taking placein Linz, Austria, October 3-7, 2011. Thevolume discusses new developments in computational methods for the simulation of flows in porous media with applications in waste storage, CO2 sequestration and fuel cells. It records the achievements of Workshop 1 ""Simulation of Flow in Porous Media and Applications in Waste Management and CO2 Sequestration"". Itbrings together key numerical mathematiciansfrom the fields ofanalysis a.
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