Bøger i Scientific Computation serien

This book deals with Random Walk Methods for solving multidimensional boundary value problems. Some of the advantages of our new methods as compared to conventional numerical methods are that they cater for stochasticities in the boundary value problems and complicated shapes of the boundaries.

The treatment of the approximation of gas dynamic equations focuses on the question of how to characterize the typical features of difference equations on the basis of the related differential approximation, which can be discussed using the fully developed theory of partial differential equations.

As a result of the numerical simulation of multidimensional gas dynamics problems on a computer, the output information is obtained in the form of immense arrays of numerical data.

Contains unique recent developments of various finite elements such as nonconforming, mixed, discontinuous, characteristic, and adaptive finite elements, along with their applications.

"To my knowledge [this] is the first book to address specifically the use of high-order discretizations in the time domain to solve wave equations. [...] I recommend the book for its clear and cogent coverage of the material selected by its author." --Physics Today, March 2003

This monograph is intended as a concise and self-contained guide for practitioners and graduate students to applying approaches in computational fluid dynamics (CFD) to real-world problems that require a quantification of viscous incompressible flows.

This book presents applications of spectral methods to problems of uncertainty propagation and quantification in model-based computations, focusing on the computational and algorithmic features of these methods most useful in dealing with models based on partial differential equations, in particular models arising in simulations of fluid flows.

This is a fully revised and updated second edition of the introduction to structured and unstructured grid methods in scientific computing. It formulates basic local and integral grid quality measures and reviews fresh approaches to mesh generation.

This book addresses stochastic optimization procedures in a broad manner. Written primarily with scientists and students from the physical and engineering sciences in mind, this book addresses a larger community of all who wish to learn about stochastic optimization techniques and how to use them.

This book addresses both the fundamentals and the practical industrial applications of Large Eddy Simulation (LES) in order to bridge the gap between LES research and the growing need to use it in engineering modeling.

The book gives the reader the basis for understanding the way numerical schemes achieve accurate and stable simulations of physical phenomena. The book builds on simple model equations and, pedagogically, on a host of problems given together with their solutions.

A comprehensive description of hybrid plasma simulation models providing a very useful summary and guide to the vast literature on this topic.

The LES-method is rapidly developing in many practical applications in engineeringThe mathematical background is presented here for the first time in book form by one of the leaders in the field

A companion to "Fundamentals in Single Domains", which discusses the fundamentals of the approximation of solutions to ordinary and partial differential equations on single domains by expansions in global basis functions. This book contains a survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries.

This monograph addresses fundamental aspects of mathematical modeling and numerical solution methods of electromagnetic problems involving low frequencies. It includes a large list of industrial applications with their mathematical formulations.

This book is about computational methods based on operator splitting.

This book is primarily intended as a research monograph that could also be used in graduate courses for the design of parallel algorithms in matrix computations.It assumes general but not extensive knowledge of numerical linear algebra, parallel architectures, and parallel programming paradigms. The book consists of four parts: (I) Basics; (II) Dense and Special Matrix Computations; (III) Sparse Matrix Computations; and (IV) Matrix functions and characteristics. Part I deals with parallel programming paradigms and fundamental kernels, including reordering schemes for sparse matrices. Part II is devoted to dense matrix computations such as parallel algorithms for solving linear systems, linear least squares, the symmetric algebraic eigenvalue problem, and the singular-value decomposition. It also deals with the development of parallel algorithms for special linear systems such as banded ,Vandermonde ,Toeplitz ,and block Toeplitz systems. Part III addresses sparsematrix computations: (a) the development of parallel iterative linear system solvers with emphasis on scalable preconditioners, (b) parallel schemes for obtaining a few of the extreme eigenpairs or those contained in a given interval in the spectrum of a standard or generalized symmetric eigenvalue problem, and (c) parallel methods for computing a few of the extreme singular triplets. Part IV focuses on the development of parallel algorithms for matrix functions and special characteristics such as the matrix pseudospectrum and the determinant. The book also reviews the theoretical and practical background necessary when designing these algorithms and includes an extensive bibliography that will be useful to researchers and students alike. The book brings together many existing algorithms for the fundamental matrix computations that have a proven track record of efficient implementation in terms of data locality and data transfer on state-of-the-art systems, as well as several algorithms that are presented for the first time, focusing on the opportunities for parallelism and algorithm robustness.

This monograph presents numerical methods for solving transient wave equations (i.e.

This book is about computational methods based on operator splitting.

This monograph presents numerical methods for solving transient wave equations (i.e.

This book presents a new method of asymptotic analysis of boundary-layer problems, the Successive Complementary Expansion Method (SCEM). The second part is devoted to SCEM and its applications in fluid mechanics, including external and internal flows.

In this step-by-step guide to numerical simulations of complex transport phenomena, now in an updated second edition, the authors provide an in-depth presentation of modern FCT algorithms as well as the range of criteria underlying their design.

The study of optimal shape design can be arrived at by asking the following question: "What is the best shape for a physical system?" Each of these fields is reviewed briefly: PDEs (Chapter 1), optimization (Chapter 4), optimal control (Chapter 5), and numerical methods (Chapters 1 and 4).

This book describes the mathematical background and reviews the techniques for solving problems, including those that require large computations such as transonic flows for compressible fluids and the Navier-Stokes equations for incompressible viscous fluids.

Flux Coordinates and Magnetic Field Structure gives a systematic and rigorous presentation of the mathematical framework and principles underlying the description of magnetically confined fusion plasmas.

The second half of the book covers the treatment of a variety of steady flow problems, including effects of both viscosity and compressibi lity, by the Method of Integral Relations, Telenin's Method, and the Method of Lines.

Book) 2 Computational Techniques for Solution of Convective Equations 5 (D. 2 Requirements for Convective Equation Algorithms 7 2. 3 Quasiparticle Methods 10 2. 4 Characteristic Methods 13 2. 5 Finite-Difference Methods 15 2. 2 ETBFCT: A Fully Vectorized FCT Module 33 3. 2 Time Integration Schemes for Barotropic Models 58 4.