By Christoph Überhuber

ISBN-10: 3540591516

ISBN-13: 9783540591511

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By Christoph Überhuber

ISBN-10: 3540591516

ISBN-13: 9783540591511

Das vorliegende Buch er6rtert - ohne Anspruch auf Vollstandigkeit - zahlreiche Aspekte des computerunterstiitzten numerischen L6sens natur- und ingenieur wissenschaftlicher Aufgaben. Dem multidisziplinaren Charakter der desktop Numerik entsprechend werden dabei verschiedene Gebiete angesprochen: von der Angewandten und Numerischen Mathematik iiber die Numerische Datenverar beitung bis zur Systemsoftware und Rechnerarchitektur. Angewandte Mathematik I I I Numerische Mathematik I Symbolische Mathematik I Numerische Dateoverarbeitung I Symbolische Datenverarbeitung Systemsoftware Die Behandlung der verschiedenen Themen der Computer-Numerik ist am An fang jedes Abschnitts eine induktive: Von speziellen praktischen Beispielen aus gehend wird zu allgemeingiiltigen mathematischen Problemformulierungen iiber geleitet. Auf dieser abstrakten Ebene werden dann Prinzipien und Methoden zur algorithmisch-numerischen L6sung der entsprechenden mathematischen professional bleme behandelt, Genauigkeit und Effizienz relevanter Algorithmen diskutiert sowie existierende Implementierungen in vorhandener numerischer software program vor gestellt und bewertet. In deduktiver Weise wird anhand von etwa 500 Beispielen erlautert, wie guy die allgemeinen GesetzmaBigkeiten und methodischen Prin zipien auf spezielle Aufgaben anwendet und wie guy algorithmisch und durch den Einsatz geeigneter Numerik-Software nach praktisch brauchbaren L6sungen sucht. Es wird auch eingehend darauf hingewiesen, welche Schwierigkeiten dabei unter Umstanden auftreten k6nnen und wie guy diese iiberwindet. Der Umfang und die Vielfalt der verfiigbaren software program auf dem Gebiet der Nu merik ist so groB, daB guy einen strukturierten Uberblick und gute Hintergrund info ben6tigt, urn im konkreten Anwendungsfall eine sinnvolle Auswahl treffen zu k6nnen. Unterstiitzung in dieser schwierigen state of affairs bietet das vorlie gende Buch durch eine iiberblicksartige Darstellung der verfiigbaren numerischen Software.

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By Are Magnus Bruaset,Aslak Tveito

ISBN-10: 3540290761

ISBN-13: 9783540290766

This booklet surveys the foremost issues which are necessary to high-performance simulation on parallel pcs or computational clusters. those issues, together with programming types, load balancing, mesh new release, effective numerical solvers, and medical software program, are very important constituents within the learn fields of machine technological know-how, numerical research, and medical computing. as well as offering the technological foundation, this quantity addresses chosen functions that mix assorted concepts in an effort to meet tough computational demanding situations. via contributions from a variety of across the world said specialists, this booklet offers a to-the-point and self-containing evaluation of effective how one can care for large-scale simulation problems.

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By Alberto Bressan,Denis Serre,Mark Williams,Kevin Zumbrun,Pierangelo Marcati

ISBN-10: 354072186X

ISBN-13: 9783540721864

This quantity comprises 4 lecture classes via Bressan, Serre, Zumbrun and Williams and an academic by way of Bressan at the middle Manifold Theorem. Bressan introduces the vanishing viscosity process and obviously explains the development blocks of the idea. Serre makes a speciality of lifestyles and balance for discrete surprise profiles. The lectures through Williams and Zumbrun care for the steadiness of multidimensional fronts.

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By Daniel Kressner

ISBN-10: 3540245464

ISBN-13: 9783540245469

This publication is ready computing eigenvalues, eigenvectors, and invariant subspaces of matrices. therapy comprises generalized and established eigenvalue difficulties and all very important facets of eigenvalue computations. a special characteristic is the distinctive remedy of based eigenvalue difficulties, supplying perception on accuracy and potency profits to be anticipated from algorithms that take the constitution of a matrix into account.

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By Yuli Eidelman,Israel Gohberg,Iulian Haimovici

ISBN-10: 3034806051

ISBN-13: 9783034806053

This two-volume paintings provides a scientific theoretical and computational research of various kinds of generalizations of separable matrices. the most recognition is paid to quickly algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and significant other shape. The paintings is concentrated on algorithms of multiplication, inversion and outline of eigenstructure and encompasses a huge variety of illustrative examples through the varied chapters. the 1st quantity involves 4 elements. the 1st half is of a commonly theoretical personality introducing and studying the quasiseparable and semiseparable representations of matrices and minimum rank of completion difficulties. 3 extra completions are taken care of within the moment part. The first purposes of the quasiseparable and semiseparable constitution are integrated within the 3rd half the place the interaction among the quasiseparable constitution and discrete time various linear structures with boundary stipulations play a necessary position. The fourth half includes factorization and inversion quick algorithms for matrices through quasiseparable and semiseparable constitution. The work is primarily based on effects got by way of the authors and their coauthors. as a result of its many major functions and the obtainable variety the textual content can be priceless to engineers, scientists, numerical analysts, laptop scientists and mathematicians alike.

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By Wilhelm Rust

ISBN-10: 3319133799

ISBN-13: 9783319133799

ISBN-10: 3319342614

ISBN-13: 9783319342610

This monograph describes the numerical research of non-linearities in structural mechanics, i.e. huge rotations, huge pressure (geometric non-linearities), non-linear fabric behaviour, specifically elasto-plasticity in addition to time-dependent behaviour, and get in touch with. according to that, the ebook treats balance difficulties and limit-load analyses, in addition to non-linear equations of a giant variety of variables. additionally, the writer provides quite a lot of challenge units and their ideas. the objective viewers essentially contains complicated undergraduate and graduate scholars of mechanical and civil engineering, however the booklet can also be helpful for working towards engineers in industry.

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By George Em Karniadakis,Ali Beskok,Narayan Aluru

ISBN-10: 0387221972

ISBN-13: 9780387221977

Subject sector has witnessed explosive progress over the last decade and the know-how is progressing at an astronomical rate.

Previous variation used to be first to concentration solely on circulation physics inside of microdevices. It offered over 900 copies in North the USA due to the fact that 11/01.

New variation is forty percentage longer, with 4 new chapters on contemporary issues together with Nanofluidics.

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By Yalchin Efendiev,Thomas Y. Hou

ISBN-10: 0387094954

ISBN-13: 9780387094953

ISBN-10: 0387094962

ISBN-13: 9780387094960

the purpose of this monograph is to explain the most suggestions and up to date - vances in multiscale ?nite aspect tools. This monograph is meant for thebroaderaudienceincludingengineers,appliedscientists,andforthosewho have an interest in multiscale simulations. The booklet is meant for graduate scholars in utilized arithmetic and people drawn to multiscale compu- tions. It combines a pragmatic advent, numerical effects, and research of multiscale ?nite aspect tools. as a result of the web page issue, the cloth has been condensed. each one bankruptcy of the ebook starts off with an creation and outline of the proposed equipment and motivating examples. a few new innovations are brought utilizing formal arguments which are justi?ed later within the final bankruptcy. Numerical examples demonstrating the signi?cance of the proposed tools are provided in every one bankruptcy following the outline of the equipment. within the final bankruptcy, we examine a number of consultant instances with the target of demonstrating the most errors assets and the convergence of the proposed equipment. a quick define of the ebook is as follows. The ?rst bankruptcy supplies a common introductiontomultiscalemethodsandanoutlineofeachchapter.Thesecond bankruptcy discusses the most suggestion of the multiscale ?nite point technique and its extensions. This bankruptcy additionally provides an summary of multiscale ?nite point equipment and different similar tools. The 3rd bankruptcy discusses the ext- sion of multiscale ?nite aspect how you can nonlinear difficulties. The fourth bankruptcy makes a speciality of multiscale equipment that use constrained international information.

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By Mario Bebendorf

ISBN-10: 3540771468

ISBN-13: 9783540771463

Hierarchical matrices are a good framework for large-scale absolutely populated matrices bobbing up, e.g., from the finite point discretization of resolution operators of elliptic boundary price difficulties. as well as storing such matrices, approximations of the standard matrix operations should be computed with logarithmic-linear complexity, which are exploited to setup approximate preconditioners in a good and handy manner. in addition to the algorithmic facets of hierarchical matrices, the most target of this e-book is to offer their theoretical background.

The booklet comprises the present approximation concept for elliptic difficulties together with partial differential operators with nonsmooth coefficients. in addition, it provides in complete element the adaptive pass approximation process for the effective remedy of indispensable operators with non-local kernel services. the idea is supported by means of many numerical experiments from genuine applications.

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By John Neuberger

ISBN-10: 3642040403

ISBN-13: 9783642040405

A Sobolev gradient of a real-valued sensible on a Hilbert area is a gradient of that sensible taken relative to an underlying Sobolev norm. This publication exhibits how descent equipment utilizing such gradients permit a unified therapy of a large choice of difficulties in differential equations. For discrete models of partial differential equations, corresponding Sobolev gradients are obvious to be drastically extra effective than usual gradients. in truth, descent tools with those gradients regularly scale linearly with the variety of grid issues, in sharp distinction with using traditional gradients. apart from the 1st variation of this paintings, this is often the one recognized account of Sobolev gradients in booklet shape.

Most of the functions during this e-book have emerged because the first version used to be released a few twelve years in the past. What continues to be of the 1st variation has been greatly revised. there are many plots of effects from calculations and a pattern MatLab code is incorporated for an easy challenge. these operating via a good element of the cloth have some time past been capable of use the idea all alone purposes and likewise achieve an appreciation of the potential for a slightly complete viewpoint near to partial differential equations.

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