Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. The reader finds here an elementary introduction to multi-grid algorithms as well as a comprehensive convergence analysis. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.). The book also contains a complete presentation of the multi-grid method of the second kind, which has important applications to integral equations (e.g. the "panel method") and to numerous other problems. Readers with a practical interest in...
Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. The reader finds here an elementary introduction to m...
Computing application to materials science is one of the fastest-growing research areas. This book introduces the concepts and methodologies related to the modeling of the complex phenomena occurring in materials processing. It is intended for undergraduate and graduate students in materials science and engineering, mechanical engineering and physics, and for engineering professionals or researchers.
Computing application to materials science is one of the fastest-growing research areas. This book introduces the concepts and methodologies relate...
This book has developed from lectures that the author gave for mathematics students at the Ruhr-Universitat Bochum and the Christian-Albrechts-Uni- versitat Kiel. This edition is the result of the translation and correction of the German edition entitled Theone und Numenk elliptischer Differential- gleichungen. The present work is restricted to the theory of partial differential equa- tions of elliptic type, which otherwise tends to be given a treatment which is either too superficial or too extensive. The following sketch shows what the problems are for elliptic differential equations. A:...
This book has developed from lectures that the author gave for mathematics students at the Ruhr-Universitat Bochum and the Christian-Albrechts-Uni- ve...
This book is a revised version of the first edition, regarded as a classic in its field. In some places, newer research results have been incorporated in the revision, and in other places, new material has been added to the chapters in the form of additional up-to-date references and some recent theorems to give readers some new directions to pursue.
This book is a revised version of the first edition, regarded as a classic in its field. In some places, newer research results have been incorpora...
This book deals with numerical methods for solving partial differential equa- tions (PDEs) coupling advection, diffusion and reaction terms, with a focus on time-dependency. A combined treatment is presented of methods for hy- perbolic problems, thereby emphasizing the one-way wave equation, meth- ods for parabolic problems and methods for stiff and non-stiff ordinary dif- ferential equations (ODEs). With regard to time-dependency we have at- tempted to present the algorithms and the discussion of their properties for the three different types of differential equations in a unified way by...
This book deals with numerical methods for solving partial differential equa- tions (PDEs) coupling advection, diffusion and reaction terms, with a fo...
The analysis of singular perturbed di?erential equations began early in the twentieth century, when approximate solutions were constructed from asy- totic expansions. (Preliminary attempts appear in the nineteenth century see vD94].)Thistechniquehas?ourishedsincethemid-1960sanditsprincipal ideas and methods are described in several textbooks; nevertheless, asy- totic expansions may be impossible to construct or may fail to simplify the given problem and then numerical approximations are often the only option. Thesystematicstudyofnumericalmethodsforsingularperturbationpr- lems started somewhat...
The analysis of singular perturbed di?erential equations began early in the twentieth century, when approximate solutions were constructed from asy- t...
This book is a revised version of the first edition, regarded as a classic in its field. In some places, newer research results have been incorporated in the revision, and in other places, new material has been added to the chapters in the form of additional up-to-date references and some recent theorems to give readers some new directions to pursue.
This book is a revised version of the first edition, regarded as a classic in its field. In some places, newer research results have been incorpora...
Computing application to materials science is one of the fastest-growing research areas. This book introduces the concepts and methodologies related to the modeling of the complex phenomena occurring in materials processing. It is intended for undergraduate and graduate students in materials science and engineering, mechanical engineering and physics, and for engineering professionals or researchers.
Computing application to materials science is one of the fastest-growing research areas. This book introduces the concepts and methodologies relate...
This book deals with numerical methods for solving partial differential equa- tions (PDEs) coupling advection, diffusion and reaction terms, with a focus on time-dependency. A combined treatment is presented of methods for hy- perbolic problems, thereby emphasizing the one-way wave equation, meth- ods for parabolic problems and methods for stiff and non-stiff ordinary dif- ferential equations (ODEs). With regard to time-dependency we have at- tempted to present the algorithms and the discussion of their properties for the three different types of differential equations in a unified way by...
This book deals with numerical methods for solving partial differential equa- tions (PDEs) coupling advection, diffusion and reaction terms, with a fo...
Stochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a mathematical description of classical direct simulation Monte Carlo (DSMC) procedures for rarefied gases, using the theory of Markov processes as a unifying framework. The second goal is a systematic treatment of an extension of DSMC, called stochastic weighted particle method. This method includes several new features, which are introduced for the purpose of variance reduction (rare event simulation). Rigorous convergence results as well as...
Stochastic numerical methods play an important role in large scale computations in the applied sciences. The first goal of this book is to give a m...
