Computational Mathematics, Mitsotakis, Dimitrios

Автор: Joachim Gwinner , Ernst Peter Stephan
Название: Advanced Boundary Element Methods
ISBN: 3319920006 ISBN-13(EAN): 9783319920009
Издательство: Springer
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Цена: 83850.00 T
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Описание: This book is devoted to the mathematical analysis of the numerical solution of boundary integral equations treating boundary value, transmission and contact problems arising in elasticity, acoustic and electromagnetic scattering. It serves as the mathematical foundation of the boundary element methods (BEM) both for static and dynamic problems. The book presents a systematic approach to the variational methods for boundary integral equations including the treatment with variational inequalities for contact problems.

It also features adaptive BEM, hp-version BEM, coupling of finite and boundary element methods - efficient computational tools that have become extremely popular in applications. Familiarizing readers with tools like Mellin transformation and pseudodifferential operators as well as convex and nonsmooth analysis for variational inequalities, it concisely presents efficient, state-of-the-art boundary element approximations and points to up-to-date research. The authors are well known for their fundamental work on boundary elements and related topics, and this book is a major contribution to the modern theory of the BEM (especially for error controlled adaptive methods and for unilateral contact and dynamic problems) and is a valuable resource for applied mathematicians, engineers, scientists and graduate students.

Автор: Hairer Ernst, Wanner Gerhard
Название: Solving Ordinary Differential Equations II / Stiff and Differential-Algebraic Problems
ISBN: 3540604529 ISBN-13(EAN): 9783540604525
Издательство: Springer
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Цена: 149060.00 T
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Описание: The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). The book is divided into four chapters. The beginning of each chapter is of introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on the order and accuracy, linear and nonlinear stability, convergence and asymptotic expansions. Stiff and differential-algebraic problems arise everywhere in scientific computations (e.g., in physics, chemistry, biology, control engineering, electrical network analysis, mechanical systems). Many applications as well as computer programs are presented.

Автор: Hoffman, Johan,
Название: Methods in computational science /
ISBN: 1611976715 ISBN-13(EAN): 9781611976717
Издательство: Mare Nostrum (Eurospan)
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Цена: 74410.00 T
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Описание: Computational methods are an integral part of most scientific disciplines, and a rudimentary understanding of their potential and limitations is essential for any scientist or engineer. This textbook introduces computational science through a set of methods and algorithms with the aim of familiarizing the reader with the field's theoretical foundations and providing the practical skills to use and develop computational methods. Methods in Computational Scienceextends the classical syllabus with new material, including high performance computing, adjoint methods, machine learning, randomized algorithms, and quantum computing,is centered around a set of fundamental algorithms presented in the form of pseudocode,presents theoretical material alongside several examples and exercises, andprovides Python implementations of many key algorithms.Methods in Computational Science is a textbook for computer science and data science students at the advanced undergraduate and graduate level. It is appropriate for the following courses: Advanced Numerical Analysis, Special Topics on Numerical Analysis, Topics on Data Science, Topics on Numerical Optimization, and Topics on Approximation Theory. Because the text is self-contained, it can also be used to support continuous learning for practicing mathematicians, data scientists, computer scientists, and engineers in the field of computational science.

Автор: Hairer, E.
Название: Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations
ISBN: 3540306633 ISBN-13(EAN): 9783540306634
Издательство: Springer
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Цена: 149060.00 T
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Описание: This book covers numerical methods that preserve properties of Hamiltonian systems, reversible systems, differential equations on manifolds and problems with highly oscillatory solutions. The long-time behavior of the numerical solutions is studied using a backward error analysis combined with KAM theory.

Автор: Schoenmaker Wim
Название: Computational Electrodynamics: A Gauge Approach with Applications in Microelectronics
ISBN: 8793519842 ISBN-13(EAN): 9788793519848
Издательство: Taylor&Francis
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Цена: 88800.00 T
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Описание: Computational Electrodynamics is a vast research field with a wide variety of tools. In physics the principle of gauge invariance plays a pivotal role as a guide towards a sensible formulation of the laws of nature as well as computing the properties of elementary particles using the lattice formulation of gauge theories, yet the gauge principle has played a much less pronounced role in performing computation in classical electrodynamics. In this work the author will demonstrate that starting from the gauge formulation of electrodynamics using the electromagnetic potentials leads to computational tools that can very well compete with the conventional electromagnetic field-based tools. Once accepting the formulation based on gauge fields, the computational code is very transparent due to the mimetic mapping of the electrodynamic variables on the computational grid. Although the illustrations and applications originate from microelectronic engineering, the method has a much larger range of applicability. Therefore this book is of interest to everyone having interest in computational electrodynamics. The volume is organized as follows: In part 1, a detailed introduction and overview is presented of the Maxwell equations as well as the derivation of the current and charge densities is different materials. Semiconductors are responding to electromagnetic fields in a non-linear way and the induced complications are discussed in detail. In part 2, the transition of the theory of electrodynamics, using the gauge potentials, to a formulation that can serve as the gateway to computational code is presented. In part 3, the feasibility and success of the methods of part 2 are demonstrated by a collection of microelectronic device designs. Part 4 focuses on a set of topical themes that brings the reader to the frontier of research in building the simulation tools using the gauge principle in computational electrodynamics.Technical topics discussed in the book include:Electromagnetic Field EquationsConstitutive RelationsDiscretization and Numerical AnalysisFinite Element and Finite Volume MethodsDesign of Integrated Passive Components.

Автор: Hackbusch
Название: Tensor Spaces and Numerical Tensor Calculus
ISBN: 3642280269 ISBN-13(EAN): 9783642280269
Издательство: Springer
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Цена: 121110.00 T
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Описание: Special numerical techniques are already needed to deal with nxn matrices for large n.Tensor data are of size nxnx...xn=n^d, where n^d exceeds the computer memory by far. They appear for problems of high spatial dimensions. Since standard methods fail, a particular tensor calculus is needed to treat such problems. The monograph describes the methods how tensors can be practically treated and how numerical operations can be performed. Applications are problems from quantum chemistry, approximation of multivariate functions, solution of pde, e.g., with stochastic coefficients, etc. ?

Автор: Butcher John C.
Название: B-Series: Algebraic Analysis of Numerical Methods
ISBN: 3030709582 ISBN-13(EAN): 9783030709587
Издательство: Springer
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Цена: 121110.00 T
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Описание: Chapter six, on multivalue methods, gives a traditional review of linear multistep methods and expands this to general linear methods, for which the B-series approach is both natural and essential.

Автор: Thomas Huckle, Tobias Neckel
Название: Bits and Bugs: A Scientific and Historical Review of Software Failures in Computational Science
ISBN: 1611975557 ISBN-13(EAN): 9781611975550
Издательство: Mare Nostrum (Eurospan)
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Цена: 38450.00 T
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Описание: In scientific computing (also known as computational science), advanced computing capabilities are used to solve complex problems. This self-contained book describes and analyzes reported software failures related to the major topics within scientific computing: mathematical modeling of phenomena; numerical analysis (number representation, rounding, conditioning); mathematical aspects and complexity of algorithms, systems, or software; concurrent computing (parallelization, scheduling, synchronization); and numerical data (such as input of data and design of control logic).Readers will find lists of related, interesting bugs, MATLAB examples, and ""excursions"" that provide necessary background, as well as an in-depth analysis of various aspects of the selected bugs. Illustrative examples of numerical principles such as machine numbers, rounding errors, condition numbers, and complexity are also included.This book is intended for students, teachers, and researchers in scientific computing, computer science, and applied mathematics. It is also an entertaining and motivating introduction for those with a minimum background in mathematics or computer science. Bits and Bugs can be used for courses in numerical analysis, numerical methods in linear algebra/ODEs/PDEs, introductory software engineering, introductory scientific computing, and parallel programming.

Автор: White, Robert E. (north Carolina State University, Raleigh, Usa)
Название: Computational linear algebra
ISBN: 1032302461 ISBN-13(EAN): 9781032302461
Издательство: Taylor&Francis
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Цена: 45930.00 T
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Описание: This unique textbook presents a course on computational linear algebra. Offers many unique applications. MATLAB is used throughout.

Автор: Eberhard Baensch
Название: Challenges in Scientific Computing - CISC 2002
ISBN: 3642624065 ISBN-13(EAN): 9783642624063
Издательство: Springer
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Цена: 93160.00 T
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Описание: This proceedings comprises 13 papers form the conference, ranging from numerical methods for flow problems, multigrid methods, semiconductor and microwave simulation, solution methods, finite element analysis to software aspects.

Автор: E. J. Hinch
Название: Think Before You Compute: A Prelude to Computational Fluid Dynamics
ISBN: 1108479545 ISBN-13(EAN): 9781108479547
Издательство: Cambridge Academ
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Цена: 122460.00 T
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Описание: This guide to computational fluid mechanics is for any beginning graduate student who is thinking of computing a flow. The text starts with a quick introduction to enable students to solve numerically a simple problem by a simple method, before detailing all the key essentials and discussing optional advanced topics.

Автор: Adcock, Ben Brugiapaglia, Simone Webster, Clayton G.
Название: Sparse polynomial approximation of high-dimensional functions
ISBN: 1611976871 ISBN-13(EAN): 9781611976878
Издательство: Mare Nostrum (Eurospan)
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Цена: 70230.00 T
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Описание: Over seventy years ago, Richard Bellman coined the term "the curse of dimensionality" to describe phenomena and computational challenges that arise in high dimensions. These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data. This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods. These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering. It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations. It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques.Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing. It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code. The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book's companion website (www.sparse-hd-book.com).This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.