Adaptive Methods Of Computing Mathematics And Mechanics

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Adaptive Methods Of Computing Mathematics And Mechanics Stochastic Variant

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Author : D G Arsenjev
language : en
Publisher: World Scientific
Release Date : 1999-04-19

Adaptive Methods Of Computing Mathematics And Mechanics Stochastic Variant written by D G Arsenjev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-04-19 with Mathematics categories.

This book describes adaptive methods of statistical numerical analysis using evaluation of integrals, solution of integral equations, boundary value problems of the theory of elasticity and heat conduction as examples.The results and approaches provided in this book are different from those available in the literature as detailed descriptions of the mechanisms of adaptation of statistical evaluation procedures, which accelerate their convergence, are given.

Adaptive Stochastic Methods

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Author : Dmitry G. Arseniev
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-01-09

Adaptive Stochastic Methods written by Dmitry G. Arseniev and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-09 with Mathematics categories.

This monograph develops adaptive stochastic methods in computational mathematics. The authors discuss the basic ideas of the algorithms and ways to analyze their properties and efficiency. Methods of evaluation of multidimensional integrals and solutions of integral equations are illustrated by multiple examples from mechanics, theory of elasticity, heat conduction and fluid dynamics. Contents Part I: Evaluation of Integrals Fundamentals of the Monte Carlo Method to Evaluate Definite Integrals Sequential Monte Carlo Method and Adaptive Integration Methods of Adaptive Integration Based on Piecewise Approximation Methods of Adaptive Integration Based on Global Approximation Numerical Experiments Adaptive Importance Sampling Method Based on Piecewise Constant Approximation Part II: Solution of Integral Equations Semi-Statistical Method of Solving Integral Equations Numerically Problem of Vibration Conductivity Problem on Ideal-Fluid Flow Around an Airfoil First Basic Problem of Elasticity Theory Second Basic Problem of Elasticity Theory Projectional and Statistical Method of Solving Integral Equations Numerically

Adaptive Stochastic Methods

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Author : Dmitriĭ Germanovich Arsenʹev
language : en
Publisher: de Gruyter
Release Date : 2018

Adaptive Stochastic Methods written by Dmitriĭ Germanovich Arsenʹev and has been published by de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Mathematics categories.

"This monograph is devoted to developing adaptive stochastic methods of computational mathematics with the use of adaptively controlled computational procedures. We consider the base ideas of the algorithms, ways to synthesise them, and analyse their properties and efficiency while evaluating multidimensional integrals and solving integral equations of the theory of elasticity and the theory of heat conduction. The key feature of the approaches and results presented in this book consists of a comprehensive analysis of mechanisms of utilisation of adaptive control in statistical evaluation procedures, which makes them converge much faster. This book is intended for all students of numerical methods, mathematical statistics, and methods of statistical simulation, as well as for specialists in the fields of computational mathematics and mechanics"--Page v.

Adaptive Methods Of Computing Mathematics And Mechanics

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Author : Dmitrij G. Arsen'ev
language : en
Publisher: World Scientific
Release Date : 1999

Adaptive Methods Of Computing Mathematics And Mechanics written by Dmitrij G. Arsen'ev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

This book describes adaptive methods of statistical numerical analysis using evaluation of integrals, solution of integral equations, boundary value problems of the theory of elasticity and heat conduction as examples. The results and approaches provided in this book are different from those available in the literature as detailed descriptions of the mechanisms of adaptation of statistical evaluation procedures, which accelerate their convergence, are given.

Advances In Adaptive Computational Methods In Mechanics

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Author : P. Ladeveze
language : en
Publisher: Elsevier
Release Date : 1998-06-23

Advances In Adaptive Computational Methods In Mechanics written by P. Ladeveze and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-06-23 with Computers categories.

Mastering modelling, and in particular numerical models, is becoming a crucial and central question in modern computational mechanics. Various tools, able to quantify the quality of a model with regard to another one taken as the reference, have been derived. Applied to computational strategies, these tools lead to new computational methods which are called "adaptive". The present book is concerned with outlining the state of the art and the latest advances in both these important areas. Papers are selected from a Workshop (Cachan 17-19 September 1997) which is the third of a series devoted to Error Estimators and Adaptivity in Computational Mechanics. The Cachan Workshop dealt with latest advances in adaptive computational methods in mechanics and their impacts on solving engineering problems. It was centered too on providing answers to simple questions such as: what is being used or can be used at present to solve engineering problems? What should be the state of art in the year 2000? What are the new questions involving error estimators and their applications?

Research Directions In Computational Mechanics

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Author : National Research Council
language : en
Publisher: National Academies Press
Release Date : 1991-02-01

Research Directions In Computational Mechanics written by National Research Council and has been published by National Academies Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-02-01 with Technology & Engineering categories.

Computational mechanics is a scientific discipline that marries physics, computers, and mathematics to emulate natural physical phenomena. It is a technology that allows scientists to study and predict the performance of various productsâ€"important for research and development in the industrialized world. This book describes current trends and future research directions in computational mechanics in areas where gaps exist in current knowledge and where major advances are crucial to continued technological developments in the United States.

Mathematical And Computational Techniques For Multilevel Adaptive Methods

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Author : Ulrich Ruede
language : en
Publisher: SIAM
Release Date : 1993-01-01

Mathematical And Computational Techniques For Multilevel Adaptive Methods written by Ulrich Ruede and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Mathematics categories.

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.

Error Controlled Adaptive Finite Elements In Solid Mechanics

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Author : Ekkehard Ramm
language : en
Publisher: John Wiley & Sons
Release Date : 2003-08-01

Error Controlled Adaptive Finite Elements In Solid Mechanics written by Ekkehard Ramm and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-01 with Technology & Engineering categories.

Finite Element Methods are used for numerous engineering applications where numerical solutions of partial differential equations are needed. As computers can now deal with the millions of parameters used in these methods, automatic error estimation and automatic adaptation of the utilised method (according to this error estimation), has become a hot research topic. This text offers comprehensive coverage of this new field of automatic adaptation and error estimation, bringing together the work of eight outstanding researchers in this field who have completed a six year national research project within the German Science Foundation. The result is a state-of-the-art work in true reference style. Each chapter is self-contained and covers theoretical, algorithmic and software presentations as well as solved problems. A main feature consists of several carefully elaborated benchmarks of 2D- and 3D- applications. * First book to go beyond the Finite Element Method in itself * Covers material from a new research area * Presents benchmarks of 2D- and 3D- applications * Fits with the new trend for genetic strategies in engineering

Multiphysics Phase Field Fracture

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Author : Thomas Wick
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-10-12

Multiphysics Phase Field Fracture written by Thomas Wick and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-12 with Mathematics categories.

This monograph is centered on mathematical modeling, innovative numerical algorithms and adaptive concepts to deal with fracture phenomena in multiphysics. State-of-the-art phase-field fracture models are complemented with prototype explanations and rigorous numerical analysis. These developments are embedded into a carefully designed balance between scientific computing aspects and numerical modeling of nonstationary coupled variational inequality systems. Therein, a focus is on nonlinear solvers, goal-oriented error estimation, predictor-corrector adaptivity, and interface conditions. Engineering applications show the potential for tackling practical problems within the fields of solid mechanics, porous media, and fluidstructure interaction.

Adaptive Methods Algorithms Theory And Applications

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Author : W. Hackbusch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21

Adaptive Methods Algorithms Theory And Applications written by W. Hackbusch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-21 with Computers categories.

The GAMM Committee for "Efficient Numerical Methods for Partial Differential Equations" organizes workshops on subjects concerning the algorithmical treat ment of partial differential equations. The topics are discretization methods like the finite element and finite volume method for various types of applications in structural and fluid mechanics. Particular attention is devoted to advanced solu tion techniques. th The series of such workshops was continued in 1993, January 22-24, with the 9 Kiel-Seminar on the special topic "Adaptive Methods Algorithms, Theory and Applications" at the Christian-Albrechts-University of Kiel. The seminar was attended by 76 scientists from 7 countries and 23 lectures were given. The list of topics contained general lectures on adaptivity, special discretization schemes, error estimators, space-time adaptivity, adaptive solvers, multi-grid me thods, wavelets, and parallelization. Special thanks are due to Michael Heisig, who carefully compiled the contribu tions to this volume. November 1993 Wolfgang Hackbusch Gabriel Wittum v Contents Page A. AUGE, G. LUBE, D. WEISS: Galerkin/Least-Squares-FEM and Ani- tropic Mesh Refinement. 1 P. BASTIAN, G. WmUM : Adaptive Multigrid Methods: The UG Concept. 17 R. BEINERT, D. KRONER: Finite Volume Methods with Local Mesh Alignment in 2-D. 38 T. BONK: A New Algorithm for Multi-Dimensional Adaptive Nume- cal Quadrature. 54 F.A. BORNEMANN: Adaptive Solution of One-Dimensional Scalar Conservation Laws with Convex Flux. 69 J. CANU, H. RITZDORF : Adaptive, Block-Structured Multigrid on Local Memory Machines. 84 S. DAHLKE, A. KUNaTH: Biorthogonal Wavelets and Multigrid. 99 B. ERDMANN, R.H.W. HOPPE, R.