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A Hybrid Domain Decomposition Method For Advection Diffusion Problems
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Book Synopsis A Hybrid Domain Decomposition Method for Advection-diffusion Problems by : M. S. Espedal
Download or read book A Hybrid Domain Decomposition Method for Advection-diffusion Problems written by M. S. Espedal and published by . This book was released on 1996 with total page 13 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scalable Hybrid Schwarz Domain Decomposition Algorithms to Solve Advection-diffusion Problems by : Lopamudra Chakravarty
Download or read book Scalable Hybrid Schwarz Domain Decomposition Algorithms to Solve Advection-diffusion Problems written by Lopamudra Chakravarty and published by . This book was released on 2018 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The solution of the linear system of algebraic equations that arise from the finite element discretization of the advection-diffusion equation is considered here. In this dissertation, we study three hybrid Schwarz domain decomposition algorithms to solve this non-symmetric problem. We use the GMRES and BiCGStab methods to solve the resulting preconditioned system. In each iteration step, we solve a coarse finite element problem and a number of local problems depending on the algorithm. Local problems are solved in non-overlapping subdomains and ring-shaped overlapping subdomains into which the original domain is subdivided. These three algorithms combine the advantages of additive and multiplicative methods. We show that these algorithms are scalable in the sense that the rate of convergence is independent of the mesh size and the number of subdomains. The performance of these algorithms in two dimensions is illustrated by numerical experiments.
Book Synopsis A Domain Decomposition Method for the Advection-diffusion Equation by : Erik Brakkee
Download or read book A Domain Decomposition Method for the Advection-diffusion Equation written by Erik Brakkee and published by . This book was released on 1994 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stability Estimates for Hybrid Coupled Domain Decomposition Methods by : Olaf Steinbach
Download or read book Stability Estimates for Hybrid Coupled Domain Decomposition Methods written by Olaf Steinbach and published by Springer. This book was released on 2003-01-01 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition methods are a well established tool for an efficient numerical solution of partial differential equations, in particular for the coupling of different model equations and of different discretization methods. Based on the approximate solution of local boundary value problems either by finite or boundary element methods, the global problem is reduced to an operator equation on the skeleton of the domain decomposition. Different variational formulations then lead to hybrid domain decomposition methods.
Book Synopsis Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations by : Tarek Mathew
Download or read book Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations written by Tarek Mathew and published by Springer Science & Business Media. This book was released on 2008-06-25 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations. This book serves as a matrix oriented introduction to domain decomposition methodology. A wide range of topics are discussed include hybrid formulations, Schwarz, and many more.
Book Synopsis A Balancing Domain Decomposition Method by Constraints for Advection-diffusion Problems by :
Download or read book A Balancing Domain Decomposition Method by Constraints for Advection-diffusion Problems written by and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The balancing domain decomposition methods by constraints are extended to solving nonsymmetric, positive definite linear systems resulting from the finite element discretization of advection-diffusion equations. A pre-conditioned GMRES iteration is used to solve a Schur complement system of equations for the subdomain interface variables. In the preconditioning step of each iteration, a partially sub-assembled finite element problem is solved. A convergence rate estimate for the GMRES iteration is established, under the condition that the diameters of subdomains are small enough. It is independent of the number of subdomains and grows only slowly with the subdomain problem size. Numerical experiments for several two-dimensional advection-diffusion problems illustrate the fast convergence of the proposed algorithm.
Book Synopsis Third International Symposium on Domain Decomposition Methods for Partial Differential Equations by : Tony F. Chan
Download or read book Third International Symposium on Domain Decomposition Methods for Partial Differential Equations written by Tony F. Chan and published by SIAM. This book was released on 1990-01-01 with total page 518 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Adaptive Domain Decomposition Methods for Advection-diffusion Problems by : Alfio Quarteroni
Download or read book Adaptive Domain Decomposition Methods for Advection-diffusion Problems written by Alfio Quarteroni and published by . This book was released on 1993 with total page 25 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Domain Decomposition Methods by : Victorita Dolean
Download or read book An Introduction to Domain Decomposition Methods written by Victorita Dolean and published by SIAM. This book was released on 2015-12-08 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to offer an overview of the most popular domain decomposition methods for partial differential equations (PDEs). These methods are widely used for numerical simulations in solid mechanics, electromagnetism, flow in porous media, etc., on parallel machines from tens to hundreds of thousands of cores. The appealing feature of domain decomposition methods is that, contrary to direct methods, they are naturally parallel. The authors focus on parallel linear solvers. The authors present all popular algorithms, both at the PDE level and at the discrete level in terms of matrices, along with systematic scripts for sequential implementation in a free open-source finite element package as well as some parallel scripts. Also included is a new coarse space construction (two-level method) that adapts to highly heterogeneous problems.
Book Synopsis Convergence Analysis of Domain Decomposition Algorithms with Full Overlapping for the Advection-diffusion Problems by : Patrick Le Tallec
Download or read book Convergence Analysis of Domain Decomposition Algorithms with Full Overlapping for the Advection-diffusion Problems written by Patrick Le Tallec and published by . This book was released on 1996 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Domain Decomposition Methods in Science and Engineering XXIV by : Petter E. Bjørstad
Download or read book Domain Decomposition Methods in Science and Engineering XXIV written by Petter E. Bjørstad and published by Springer. This book was released on 2019-01-05 with total page 570 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are the proceedings of the 24th International Conference on Domain Decomposition Methods in Science and Engineering, which was held in Svalbard, Norway in February 2017. Domain decomposition methods are iterative methods for solving the often very large systems of equations that arise when engineering problems are discretized, frequently using finite elements or other modern techniques. These methods are specifically designed to make effective use of massively parallel, high-performance computing systems. The book presents both theoretical and computational advances in this domain, reflecting the state of art in 2017.
Book Synopsis Domain Decomposition Methods in Science and Engineering XXV by : Ronald Haynes
Download or read book Domain Decomposition Methods in Science and Engineering XXV written by Ronald Haynes and published by Springer Nature. This book was released on 2020-10-24 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are the proceedings of the 25th International Conference on Domain Decomposition Methods in Science and Engineering, which was held in St. John's, Newfoundland, Canada in July 2018. Domain decomposition methods are iterative methods for solving the often very large systems of equations that arise when engineering problems are discretized, frequently using finite elements or other modern techniques. These methods are specifically designed to make effective use of massively parallel, high-performance computing systems. The book presents both theoretical and computational advances in this domain, reflecting the state of art in 2018.
Book Synopsis Domain Decomposition Methods in Science and Engineering XXII by : Thomas Dickopf
Download or read book Domain Decomposition Methods in Science and Engineering XXII written by Thomas Dickopf and published by Springer. This book was released on 2016-03-11 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are the proceedings of the 22nd International Conference on Domain Decomposition Methods, which was held in Lugano, Switzerland. With 172 participants from over 24 countries, this conference continued a long-standing tradition of internationally oriented meetings on Domain Decomposition Methods. The book features a well-balanced mix of established and new topics, such as the manifold theory of Schwarz Methods, Isogeometric Analysis, Discontinuous Galerkin Methods, exploitation of modern HPC architectures and industrial applications. As the conference program reflects, the growing capabilities in terms of theory and available hardware allow increasingly complex non-linear and multi-physics simulations, confirming the tremendous potential and flexibility of the domain decomposition concept.
Book Synopsis A Physically Motivated Domain Decomposition for Singularly Perturbed Equations by : Institute for Computer Applications in Science and Engineering
Download or read book A Physically Motivated Domain Decomposition for Singularly Perturbed Equations written by Institute for Computer Applications in Science and Engineering and published by . This book was released on 1988 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: A domain decomposition algorithm suitable for the efficient and accurate solution of a parabolic reaction convection diffusion equation with small parameter on the diffusion term is presented. Convergence is established via maximum principle arguments. The equation arises in the modeling of laminar transonic flow. Decomposition into subdomains is accomplished via singular perturbation analysis which dictates regions where certain reduced equations may be solved in place of the full equation, effectively preconditioning the problem. This paper concentrates on the theoretical basis of the method, establishing local and global a priori error bounds. (KR).
Book Synopsis Domain Decomposition Methods in Science and Engineering by : Ralf Kornhuber
Download or read book Domain Decomposition Methods in Science and Engineering written by Ralf Kornhuber and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition is an active, interdisciplinary research area that is devoted to the development, analysis and implementation of coupling and decoupling strategies in mathematics, computational science, engineering and industry. A series of international conferences starting in 1987 set the stage for the presentation of many meanwhile classical results on substructuring, block iterative methods, parallel and distributed high performance computing etc. This volume contains a selection from the papers presented at the 15th International Domain Decomposition Conference held in Berlin, Germany, July 17-25, 2003 by the world's leading experts in the field. Its special focus has been on numerical analysis, computational issues,complex heterogeneous problems, industrial problems, and software development.
Book Synopsis Recent Developments in Domain Decomposition Methods by : Luca F. Pavarino
Download or read book Recent Developments in Domain Decomposition Methods written by Luca F. Pavarino and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this book is to provide an overview of some of the most recent developments in the field of Domain Decomposition Methods. Domain decomposition relates to the construction of preconditioners for the large algebraic systems of equations which often arise in applications, by solving smaller instances of the same problem. It also relates to the construction of approximation methods built from different discretizations in different subdomains. The resulting methods are among the most successful parallel solvers for many large scale problems in computational science and engineering. The papers in this collection reflect some of the most active research areas in domain decomposition such as novel FETI, Neumann-Neumann, overlapping Schwarz and Mortar methods.
Book Synopsis Domain Decomposition Methods in Science and Engineering XXVI by : Susanne C. Brenner
Download or read book Domain Decomposition Methods in Science and Engineering XXVI written by Susanne C. Brenner and published by Springer Nature. This book was released on 2023-03-15 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are the proceedings of the 26th International Conference on Domain Decomposition Methods in Science and Engineering, which was hosted by the Chinese University of Hong Kong and held online in December 2020. Domain decomposition methods are iterative methods for solving the often very large systems of equations that arise when engineering problems are discretized, frequently using finite elements or other modern techniques. These methods are specifically designed to make effective use of massively parallel, high-performance computing systems. The book presents both theoretical and computational advances in this domain, reflecting the state of art in 2020.