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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 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 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 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 Domain Decomposition Methods in Science and Engineering XXI by : Jocelyne Erhel
Download or read book Domain Decomposition Methods in Science and Engineering XXI written by Jocelyne Erhel and published by Springer. This book was released on 2014-10-10 with total page 931 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a selection of papers presented at the 21st international conference on domain decomposition methods in science and engineering held in Rennes, France, June 25-29, 2012. Domain decomposition is an active and interdisciplinary research discipline, focusing on the development, analysis and implementation of numerical methods for massively parallel computers. Domain decomposition methods are among the most efficient solvers for large scale applications in science and engineering. They are based on a solid theoretical foundation and shown to be scalable for many important applications. Domain decomposition techniques can also naturally take into account multiscale phenomena. This book contains the most recent results in this important field of research, both mathematically and algorithmically and allows the reader to get an overview of this exciting branch of numerical analysis and scientific computing.
Book Synopsis Domain Decomposition by : Barry Smith
Download or read book Domain Decomposition written by Barry Smith and published by Cambridge University Press. This book was released on 2004-03-25 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an easy-to-read discussion of domain decomposition algorithms, their implementation and analysis. Ideal for graduate students about to embark on a career in computational science. It will also be a valuable resource for all those interested in parallel computing and numerical computational methods.
Book Synopsis Domain Decomposition Methods - Algorithms and Theory by : Andrea Toselli
Download or read book Domain Decomposition Methods - Algorithms and Theory written by Andrea Toselli and published by Springer Science & Business Media. This book was released on 2006-06-20 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive presentation of some of the most successful and popular domain decomposition preconditioners for finite and spectral element approximations of partial differential equations. It places strong emphasis on both algorithmic and mathematical aspects. It covers in detail important methods such as FETI and balancing Neumann-Neumann methods and algorithms for spectral element methods.
Book Synopsis Domain Decomposition Methods in Science and Engineering XVI by : Olof B. Widlund
Download or read book Domain Decomposition Methods in Science and Engineering XVI written by Olof B. Widlund and published by Springer Science & Business Media. This book was released on 2007-01-19 with total page 783 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition is an active research area concerned with the development, analysis, and implementation of coupling and decoupling strategies in mathematical and computational models of natural and engineered systems. The present volume sets forth new contributions in areas of numerical analysis, computer science, scientific and industrial applications, and software development.
Book Synopsis Domain Decomposition Methods in Science and Engineering XXIII by : Chang-Ock Lee
Download or read book Domain Decomposition Methods in Science and Engineering XXIII written by Chang-Ock Lee and published by Springer. This book was released on 2017-03-15 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of papers presented at the 23rd International Conference on Domain Decomposition Methods in Science and Engineering, held on Jeju Island, Korea on July 6-10, 2015. Domain decomposition methods solve boundary value problems by splitting them into smaller boundary value problems on subdomains and iterating to coordinate the solution between adjacent subdomains. Domain decomposition methods have considerable potential for a parallelization of the finite element methods, and serve a basis for distributed, parallel computations.
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 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 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 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 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 Coercive Domain Decomposition Algorithms for Advection-diffusion Equations and Systems by : Ana Alonso
Download or read book Coercive Domain Decomposition Algorithms for Advection-diffusion Equations and Systems written by Ana Alonso and published by . This book was released on 1998 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Convergence Analysis of Domain Decomposition Algorithms with Full Overlapping for the Advection-diffusion Problems by : Institut National de Recherche en Informatique et en Automatique
Download or read book Convergence Analysis of Domain Decomposition Algorithms with Full Overlapping for the Advection-diffusion Problems written by Institut National de Recherche en Informatique et en Automatique and published by . This book was released on 1994 with total page 57 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.?
