Robust Algebraic Multilevel Methods And Algorithms

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Robust Algebraic Multilevel Methods and Algorithms

Johannes Kraus,Svetozar Margenov
Robust Algebraic Multilevel Methods and Algorithms Book PDF

Author : Johannes Kraus,Svetozar Margenov
Publisher : Walter de Gruyter
Page : 257 pages
File Size : 47,6 Mb
Release : 2009
Category : Algebras, Linear
ISBN : 9783110193657

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Robust Algebraic Multilevel Methods and Algorithms by Johannes Kraus,Svetozar Margenov Pdf

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.

Mathematical and Computational Techniques for Multilevel Adaptive Methods

Ulrich Ruede
Mathematical and Computational Techniques for Multilevel Adaptive Methods Book PDF

Author : Ulrich Ruede
Publisher : SIAM
Page : 152 pages
File Size : 53,7 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 1611970962

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Mathematical and Computational Techniques for Multilevel Adaptive Methods by Ulrich Ruede Pdf

Multilevel adaptive methods play an increasingly important role in the solution of many scientific and engineering problems. Fast adaptive methods techniques are widely used by specialists to execute and analyze simulation and optimization problems. This monograph presents a unified approach to adaptive methods, addressing their mathematical theory, efficient algorithms, and flexible data structures. Rüde introduces a well-founded mathematical theory that leads to intelligent, adaptive algorithms, and suggests advanced software techniques. This new kind of multigrid theory supports the so-called "BPX" and "multilevel Schwarz" methods, and leads to the discovery of faster more robust algorithms. These techniques are deeply rooted in the theory of function spaces. Mathematical and Computational Techniques for Multilevel Adaptive Methods examines this development together with its implications for relevant algorithms for adaptive PDE methods. The author shows how abstract data types and object-oriented programming can be used for improved implementation.

Large-Scale Scientific Computing

Ivan Lirkov,Svetozar D. Margenov,Jerzy Wasniewski
Large Scale Scientific Computing Book PDF

Author : Ivan Lirkov,Svetozar D. Margenov,Jerzy Wasniewski
Publisher : Springer
Page : 669 pages
File Size : 52,5 Mb
Release : 2012-05-24
Category : Computers
ISBN : 9783642298431

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Large-Scale Scientific Computing by Ivan Lirkov,Svetozar D. Margenov,Jerzy Wasniewski Pdf

This book constitutes the thoroughly refereed post-conference proceedings of the 8th International Conference on Large-Scale Scientific Computations, LSSC 2011, held in Sozopol, Bulgaria, in June 2011. The 74 revised full papers presented together with 3 plenary and invited papers were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on robust multigrid, multilevel and multiscale, deterministic and stochastic methods for modeling highly heterogeneous media, advanced methods for transport, control and uncertain systems, applications of metaheuristics to large-scale problems, environmental modelling, large scale computing on many-core architectures, multiscale industrial, enviromental and biomedical problems, efficient algorithms of computational geometry, high performance Monte Carlo simulations, voxel based computations and contributed papers.

Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications

Oleg P. Iliev,Svetozar D. Margenov,Peter D Minev,Panayot S. Vassilevski,Ludmil T Zikatanov
Numerical Solution of Partial Differential Equations Theory Algorithms and Their Applications Book PDF

Author : Oleg P. Iliev,Svetozar D. Margenov,Peter D Minev,Panayot S. Vassilevski,Ludmil T Zikatanov
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 40,9 Mb
Release : 2013-06-04
Category : Mathematics
ISBN : 9781461471721

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Numerical Solution of Partial Differential Equations: Theory, Algorithms, and Their Applications by Oleg P. Iliev,Svetozar D. Margenov,Peter D Minev,Panayot S. Vassilevski,Ludmil T Zikatanov Pdf

One of the current main challenges in the area of scientific computing​ is the design and implementation of accurate numerical models for complex physical systems which are described by time dependent coupled systems of nonlinear PDEs. This volume integrates the works of experts in computational mathematics and its applications, with a focus on modern algorithms which are at the heart of accurate modeling: adaptive finite element methods, conservative finite difference methods and finite volume methods, and multilevel solution techniques. Fundamental theoretical results are revisited in survey articles and new techniques in numerical analysis are introduced. Applications showcasing the efficiency, reliability and robustness of the algorithms in porous media, structural mechanics and electromagnetism are presented. Researchers and graduate students in numerical analysis and numerical solutions of PDEs and their scientific computing applications will find this book useful.

Efficient Preconditioned Solution Methods for Elliptic Partial Differential Equations

Owe Axelsson,János Karátson
Efficient Preconditioned Solution Methods for Elliptic Partial Differential Equations Book PDF

Author : Owe Axelsson,János Karátson
Publisher : Bentham Science Publishers
Page : 153 pages
File Size : 53,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9781608052912

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Efficient Preconditioned Solution Methods for Elliptic Partial Differential Equations by Owe Axelsson,János Karátson Pdf

This e-book presents several research areas of elliptical problems solved by differential equations. The mathematical models explained in this e-book have been contributed by experts in the field and can be applied to a wide range of real life examples. M

Robust Static Super-Replication of Barrier Options

Jan H. Maruhn
Robust Static Super Replication of Barrier Options Book PDF

Author : Jan H. Maruhn
Publisher : Walter de Gruyter
Page : 210 pages
File Size : 47,5 Mb
Release : 2009-07-14
Category : Mathematics
ISBN : 9783110208511

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Robust Static Super-Replication of Barrier Options by Jan H. Maruhn Pdf

Static hedge portfolios for barrier options are very sensitive with respect to changes of the volatility surface. To prevent potentially significant hedging losses this book develops a static super-replication strategy with market-typical robustness against volatility, skew and liquidity risk as well as model errors. Empirical results and various numerical examples confirm that the static superhedge successfully eliminates the risk of a changing volatility surface. Combined with associated sub-replication strategies this leads to robust price bounds for barrier options which are also relevant in the context of dynamic hedging. The mathematical techniques used to prove appropriate existence, duality and convergence results range from financial mathematics, stochastic and semi-infinite optimization, convex analysis and partial differential equations to semidefinite programming.

Fluid-Structure Interaction

Stefan Frei,Bärbel Holm,Thomas Richter,Thomas Wick,Huidong Yang
Fluid Structure Interaction Book PDF

Author : Stefan Frei,Bärbel Holm,Thomas Richter,Thomas Wick,Huidong Yang
Publisher : Walter de Gruyter GmbH & Co KG
Page : 386 pages
File Size : 55,6 Mb
Release : 2017-11-20
Category : Mathematics
ISBN : 9783110494259

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Fluid-Structure Interaction by Stefan Frei,Bärbel Holm,Thomas Richter,Thomas Wick,Huidong Yang Pdf

This monograph discusses modeling, adaptive discretisation techniques and the numerical solution of fluid structure interaction. An emphasis in part I lies on innovative discretisation and advanced interface resolution techniques. The second part covers the efficient and robust numerical solution of fluid-structure interaction. In part III, recent advances in the application fields vascular flows, binary-fluid-solid interaction, and coupling to fractures in the solid part are presented. Moreover each chapter provides a comprehensive overview in the respective topics including many references to concurring state-of-the art work. Contents Part I: Modeling and discretization On the implementation and benchmarking of an extended ALE method for FSI problems The locally adapted parametric finite element method for interface problems on triangular meshes An accurate Eulerian approach for fluid-structure interactions Part II: Solvers Numerical methods for unsteady thermal fluid structure interaction Recent development of robust monolithic fluid-structure interaction solvers A monolithic FSI solver applied to the FSI 1,2,3 benchmarks Part III: Applications Fluid-structure interaction for vascular flows: From supercomputers to laptops Binary-fluid–solid interaction based on the Navier–Stokes–Cahn–Hilliard Equations Coupling fluid-structure interaction with phase-field fracture: Algorithmic details

Numerical Methods and Applications

Ivan Dimov,Lirkov Ivan Dimov,Stefka Dimova,Natalia Kolkovska
Numerical Methods and Applications Book PDF

Author : Ivan Dimov,Lirkov Ivan Dimov,Stefka Dimova,Natalia Kolkovska
Publisher : Springer Science & Business Media
Page : 524 pages
File Size : 43,9 Mb
Release : 2011-01-14
Category : Computers
ISBN : 9783642184659

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Numerical Methods and Applications by Ivan Dimov,Lirkov Ivan Dimov,Stefka Dimova,Natalia Kolkovska Pdf

This book constitutes the thoroughly refereed post-conference proceedings of the 7th International Conference on Numerical Methods and Applications, NMA 2010, held in Borovets, Bulgaria, in August 2010. The 60 revised full papers presented together with 3 invited papers were carefully reviewed and selected from numerous submissions for inclusion in this book. The papers are organized in topical sections on Monte Carlo and quasi-Monte Carlo methods, environmental modeling, grid computing and applications, metaheuristics for optimization problems, and modeling and simulation of electrochemical processes.

Domain Decomposition Methods in Science and Engineering XX

Randolph Bank,Michael Holst,Olof Widlund,Jinchao Xu
Domain Decomposition Methods in Science and Engineering XX Book PDF

Author : Randolph Bank,Michael Holst,Olof Widlund,Jinchao Xu
Publisher : Springer Science & Business Media
Page : 702 pages
File Size : 42,7 Mb
Release : 2013-07-03
Category : Mathematics
ISBN : 9783642352751

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Domain Decomposition Methods in Science and Engineering XX by Randolph Bank,Michael Holst,Olof Widlund,Jinchao Xu Pdf

These are the proceedings of the 20th international conference on domain decomposition methods in science and engineering. Domain decomposition methods are iterative methods for solving the often very large linearor nonlinear systems of algebraic equations that arise when various problems in continuum mechanics are discretized using finite elements. They are designed for massively parallel computers and take the memory hierarchy of such systems in mind. This is essential for approaching peak floating point performance. There is an increasingly well developed theory whichis having a direct impact on the development and improvements of these algorithms.​

Scalable Algorithms for Contact Problems

Zdeněk Dostál,Tomáš Kozubek,Marie Sadowská,Vít Vondrák
Scalable Algorithms for Contact Problems Book PDF

Author : Zdeněk Dostál,Tomáš Kozubek,Marie Sadowská,Vít Vondrák
Publisher : Springer Nature
Page : 447 pages
File Size : 41,7 Mb
Release : 2023-11-29
Category : Mathematics
ISBN : 9783031335808

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Scalable Algorithms for Contact Problems by Zdeněk Dostál,Tomáš Kozubek,Marie Sadowská,Vít Vondrák Pdf

This book presents a comprehensive treatment of recently developed scalable algorithms for solving multibody contact problems of linear elasticity. The brand-new feature of these algorithms is their theoretically supported numerical scalability (i.e., asymptotically linear complexity) and parallel scalability demonstrated in solving problems discretized by billions of degrees of freedom. The theory covers solving multibody frictionless contact problems, contact problems with possibly orthotropic Tresca’s friction, and transient contact problems. In addition, it also covers BEM discretization, treating jumping coefficients, floating bodies, mortar non-penetration conditions, etc. This second edition includes updated content, including a new chapter on hybrid domain decomposition methods for huge contact problems. Furthermore, new sections describe the latest algorithm improvements, e.g., the fast reconstruction of displacements, the adaptive reorthogonalization of dual constraints, and an updated chapter on parallel implementation. Several chapters are extended to give an independent exposition of classical bounds on the spectrum of mass and dual stiffness matrices, a benchmark for Coulomb orthotropic friction, details of discretization, etc. The exposition is divided into four parts, the first of which reviews auxiliary linear algebra, optimization, and analysis. The most important algorithms and optimality results are presented in the third chapter. The presentation includes continuous formulation, discretization, domain decomposition, optimality results, and numerical experiments. The final part contains extensions to contact shape optimization, plasticity, and HPC implementation. Graduate students and researchers in mechanical engineering, computational engineering, and applied mathematics will find this book of great value and interest.

Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs

Josef Malek,Zdenek Strakos
Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs Book PDF

Author : Josef Malek,Zdenek Strakos
Publisher : SIAM
Page : 106 pages
File Size : 42,9 Mb
Release : 2014-12-22
Category : Mathematics
ISBN : 9781611973839

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Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs by Josef Malek,Zdenek Strakos Pdf

Preconditioning and the Conjugate Gradient Method in the Context of Solving PDEs?is about the interplay between modeling, analysis, discretization, matrix computation, and model reduction. The authors link PDE analysis, functional analysis, and calculus of variations with matrix iterative computation using Krylov subspace methods and address the challenges that arise during formulation of the mathematical model through to efficient numerical solution of the algebraic problem. The book?s central concept, preconditioning of the conjugate gradient method, is traditionally developed algebraically using the preconditioned finite-dimensional algebraic system. In this text, however, preconditioning is connected to the PDE analysis, and the infinite-dimensional formulation of the conjugate gradient method and its discretization and preconditioning are linked together. This text challenges commonly held views, addresses widespread misunderstandings, and formulates thought-provoking open questions for further research.?

Dirichlet-dirichlet Domain Decomposition Methods For Elliptic Problems: H And Hp Finite Element Discretizations

Korneev Vadim Glebiovich,Langer Ulrich
Dirichlet dirichlet Domain Decomposition Methods For Elliptic Problems H And Hp Finite Element Discretizations Book PDF

Author : Korneev Vadim Glebiovich,Langer Ulrich
Publisher : World Scientific
Page : 484 pages
File Size : 42,9 Mb
Release : 2015-01-29
Category : Mathematics
ISBN : 9789814578479

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Dirichlet-dirichlet Domain Decomposition Methods For Elliptic Problems: H And Hp Finite Element Discretizations by Korneev Vadim Glebiovich,Langer Ulrich Pdf

Domain decomposition (DD) methods provide powerful tools for constructing parallel numerical solution algorithms for large scale systems of algebraic equations arising from the discretization of partial differential equations. These methods are well-established and belong to a fast developing area. In this volume, the reader will find a brief historical overview, the basic results of the general theory of domain and space decomposition methods as well as the description and analysis of practical DD algorithms for parallel computing. It is typical to find in this volume that most of the presented DD solvers belong to the family of fast algorithms, where each component is efficient with respect to the arithmetical work. Readers will discover new analysis results for both the well-known basic DD solvers and some DD methods recently devised by the authors, e.g., for elliptic problems with varying chaotically piecewise constant orthotropism without restrictions on the finite aspect ratios.The hp finite element discretizations, in particular, by spectral elements of elliptic equations are given significant attention in current research and applications. This volume is the first to feature all components of Dirichlet-Dirichlet-type DD solvers for hp discretizations devised as numerical procedures which result in DD solvers that are almost optimal with respect to the computational work. The most important DD solvers are presented in the matrix/vector form algorithms that are convenient for practical use.

Regularization Methods in Banach Spaces

Thomas Schuster,Barbara Kaltenbacher,Bernd Hofmann,Kamil S. Kazimierski
Regularization Methods in Banach Spaces Book PDF

Author : Thomas Schuster,Barbara Kaltenbacher,Bernd Hofmann,Kamil S. Kazimierski
Publisher : Walter de Gruyter
Page : 296 pages
File Size : 53,9 Mb
Release : 2012-07-30
Category : Mathematics
ISBN : 9783110255720

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Regularization Methods in Banach Spaces by Thomas Schuster,Barbara Kaltenbacher,Bernd Hofmann,Kamil S. Kazimierski Pdf

Regularization methods aimed at finding stable approximate solutions are a necessary tool to tackle inverse and ill-posed problems. Inverse problems arise in a large variety of applications ranging from medical imaging and non-destructive testing via finance to systems biology. Many of these problems belong to the class of parameter identification problems in partial differential equations (PDEs) and thus are computationally demanding and mathematically challenging. Hence there is a substantial need for stable and efficient solvers for this kind of problems as well as for a rigorous convergence analysis of these methods. This monograph consists of five parts. Part I motivates the importance of developing and analyzing regularization methods in Banach spaces by presenting four applications which intrinsically demand for a Banach space setting and giving a brief glimpse of sparsity constraints. Part II summarizes all mathematical tools that are necessary to carry out an analysis in Banach spaces. Part III represents the current state-of-the-art concerning Tikhonov regularization in Banach spaces. Part IV about iterative regularization methods is concerned with linear operator equations and the iterative solution of nonlinear operator equations by gradient type methods and the iteratively regularized Gauß-Newton method. Part V finally outlines the method of approximate inverse which is based on the efficient evaluation of the measured data with reconstruction kernels.

Mathematics in Industry

Angela Slavova
Mathematics in Industry Book PDF

Author : Angela Slavova
Publisher : Cambridge Scholars Publishing
Page : 415 pages
File Size : 43,9 Mb
Release : 2015-09-18
Category : Science
ISBN : 9781443883245

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Mathematics in Industry by Angela Slavova Pdf

In this book, a wide range of problems concerning recent achievements in the field of industrial and applied mathematics are presented. It provides new ideas and research for scientists developing and studying mathematical methods and algorithms, and researchers applying them for solving real-life problems. The importance of the computing infrastructure is unquestionable for the development of modern science. The main focus of the book is the application of mathematics to industry and science. It promotes basic research in mathematics leading to new methods and techniques useful to industry and science. The volume also considers strategy-making integration between scientists of applied mathematics and those working in applied informatics, which has potential for long-lasting integration and co-operation. The integration role is regarded here as a tool for consolidation and reinforcement of the research, education and training, and for the transfer of scientific and management knowledge. This volume operates as a medium for the exchange of information and ideas between mathematicians and other technical and scientific personnel. The book will be essential for the promotion of interdisciplinary collaboration between applied mathematics and science, engineering and technology. The main topics examined in this volume are: numerical methods and algorithms; control systems and applications; partial differential equations and real-life applications; the high performance of scientific computing; linear algebra applications; neurosciences; algorithms in industrial mathematics; equations of mathematical physics; and industrial applications of mechanics.

Theoretical Foundations and Numerical Methods for Sparse Recovery

Massimo Fornasier
Theoretical Foundations and Numerical Methods for Sparse Recovery Book PDF

Author : Massimo Fornasier
Publisher : Walter de Gruyter
Page : 351 pages
File Size : 52,9 Mb
Release : 2010-07-30
Category : Mathematics
ISBN : 9783110226157

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Theoretical Foundations and Numerical Methods for Sparse Recovery by Massimo Fornasier Pdf

The present collection is the very first contribution of this type in the field of sparse recovery. Compressed sensing is one of the important facets of the broader concept presented in the book, which by now has made connections with other branches such as mathematical imaging, inverse problems, numerical analysis and simulation. The book consists of four lecture notes of courses given at the Summer School on "Theoretical Foundations and Numerical Methods for Sparse Recovery" held at the Johann Radon Institute for Computational and Applied Mathematics in Linz, Austria, in September 2009. This unique collection will be of value for a broad community and may serve as a textbook for graduate courses. From the contents: "Compressive Sensing and Structured Random Matrices" by Holger Rauhut "Numerical Methods for Sparse Recovery" by Massimo Fornasier "Sparse Recovery in Inverse Problems" by Ronny Ramlau and Gerd Teschke "An Introduction to Total Variation for Image Analysis" by Antonin Chambolle, Vicent Caselles, Daniel Cremers, Matteo Novaga and Thomas Pock