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Nodal Discontinuous Galerkin Methods de Jan S Hesthaven

Nodal Discontinuous Galerkin Methods

Autor Jan S Hesthaven, Tim Warburton
en Limba Engleză Hardback – 18 dec 2007

Ne-a atras atenția modul în care Nodal Discontinuous Galerkin Methods transformă o teorie matematică complexă într-un instrument de calcul aplicabil, oferind o punte solidă între analiza numerică și implementarea software. Lucrarea se concentrează pe metodele de tip Galerkin discontinuu (DG-FEM), structurând materia pentru a fi accesibilă atât studenților de la nivel licență avansat, cât și cercetătorilor. Considerăm că forța acestui volum rezidă în echilibrul dintre rigoarea teoretică și pragmatismul algoritmic, fiind susținut de implementări Matlab care permit verificarea imediată a conceptelor.

Organizarea volumului reflectă o progresie pedagogică logică. Jan S Hesthaven și Tim Warburton încep cu fundamentele în spațiul unidimensional, trecând apoi prin analiza erorilor și probleme neliniare, pentru ca în a doua jumătate a cărții să extindă cadrul către dimensiuni superioare, ecuații de ordin înalt și discretizări non-conforme pe elemente curbilinii. Această abordare sistematică asigură o înțelegere profundă a proprietăților spectrale ale operatorilor DG înainte de a aborda complexitatea spațiului tridimensional.

În contextul operei autorului, această carte reprezintă o fundamentare a metodelor de discretizare, în timp ce Certified Reduced Basis Methods for Parametrized Partial Differential Equations se concentrează pe eficiența computațională și reducerea modelelor pentru ecuații cu parametri. Totodată, volumul de față extinde cadrul propus de Mathematical Aspects of Discontinuous Galerkin Methods de Daniele Antonio Di Pietro cu date noi din perspectiva implementării nodale și a algoritmilor de calcul efectiv, oferind o viziune mai orientată spre practică decât analizele pur teoretice din Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations.

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Specificații

ISBN-13: 9780387720654
ISBN-10: 0387720650
Pagini: 502
Ilustrații: XIV, 502 p.
Dimensiuni: 159 x 244 x 35 mm
Greutate: 0.95 kg
Ediția:2008 edition
Editura: Springer
Locul publicării:New York, NY, United States

Public țintă

Adult: General. Academic/professional/technical: Undergraduate. Academic/professional/technical: Postgraduate. Academic/professional/technical: Research and professional

De ce să citești această carte

Recomandăm această carte oricărui student sau cercetător care dorește să stăpânească metodele Galerkin discontinuu nu doar la nivel teoretic, ci și practic. Cititorul câștigă o metodologie clară de construcție a algoritmilor și acces la un deceniu de expertiză în codarea acestor soluții. Este resursa ideală pentru trecerea de la ecuații diferențiale parțiale la simulări numerice funcționale în Matlab.

Descriere scurtă

Mathematicsisplayinganevermoreimportantroleinthephysicalandbiol- ical sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and tea- ing, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose ofthistextbookseriesistomeetthecurrentandfutureneedsoftheseadvances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Mat- matical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs. Pasadena, California J.E. Marsden Providence, Rhode Island L. Sirovich College Park, Maryland S.S. Antman Preface The algorithms, methods, and Matlab implementations described in this text have been developed during almost a decade of collaboration. During this time we have worked to simplify the basic methods and make the ideas more accessible to a broad audience. Many people, both students and colleagues, have helped during the development of this project and we are grateful for all their suggestions and input.

Cuprins

The key ideas.- Making it work in one dimension.- Insight through theory.- Nonlinear problems.- Beyond one dimension.- Higher-order equations.- Spectral properties of discontinuous Galerkin operators.- Curvilinear elements and nonconforming discretizations.- Into the third dimension.

Recenzii

From the reviews:
"This book provides comprehensive coverage of the major aspects of the DG-FEM, from derivation, analysis and implementation of the method to simulation of application problems. It is a highly valuable volume in the literature on the DG-FEM. It is also suitable as a textbook for a graduate-level course for students in computational and applied mathematics, physics and engineering."
-Mathematical Reviews
"The book under review presents basic ideas, theoretical analysis, MATLAB implementation and applications of the DG-FEM. … The representative references quoted are useful for any reader interested in applying the method in a particular area. … This book provides comprehensive coverage of the major aspects of the DG-FEM … . It is a highly valuable volume in the literature on the DG-FEM. It is also suitable as a textbook for a graduate-level course for students in computational and applied mathematics, physics, and engineering." (Weimin Han, Mathematical Reviews, Issue 2008 k)
"This book is intended to offer a comprehensive introduction to, and an efficient implementation of discontinuous Galerkin finite element methods … . Each chapter of the book is largely self-contained and is complemented by adequate exercises. … The style of writing is clear and concise … . is an exceptionally complete and accessible reference for graduate students, researchers, and professionals in applied mathematics, physics, and engineering. It may be used in graduate-level courses, as a self-study resource, or as a research reference." (Marius Ghergu, Zentralblatt MATH, Vol. 1134 (12), 2008)

Textul de pe ultima copertă

This book discusses a family of computational methods, known as discontinuous Galerkin methods, for solving partial differential equations. While these methods have been known since the early 1970s, they have experienced an almost explosive growth interest during the last ten to fifteen years, leading both to substantial theoretical developments and the application of these methods to a broad range of problems.
These methods are different in nature from standard methods such as finite element or finite difference methods, often presenting a challenge in the transition from theoretical developments to actual implementations and applications.
This book is aimed at graduate level classes in applied and computational mathematics. The combination of an in depth discussion of the fundamental properties of the discontinuous Galerkin computational methods with the availability of extensive software allows students to gain first hand experience from the beginning without eliminating theoretical insight.
Jan S. Hesthaven is a professor of Applied Mathematics at Brown University.
Tim Warburton is an assistant professor of Applied and Computational Mathematics at Rice University.

Caracteristici

First text on DG-FEM, suitable both as a textbook and for self sudy Attention to both basic analysis and algorithmic issues Easily modified MATLAB library routines Enables 1D-3D solution of PDEs in general geometries Exercises at the end of each chapter Includes supplementary material: sn.pub/extras