Alfio Quarteroni

Claudio Canuto

M. Yousuff Hussaini

Thomas A. Zang

Following up the seminal Spectral Methods in Fluid Dynamics, Spectral Methods: Evolution to Complex Geometries and Applications to Fluid Dynamics contains an extensive survey of the essential algorithmic and theoretical aspects of spectral methods for complex geometries. These types of spectral methods were only just emerging at the time the earlier book was published. The discussion of spectral algorithms for linear and nonlinear fluid dynamics stability analyses is greatly expanded. The chapter on spectral algorithms for incompressible flow focuses on algorithms that have proven most useful in practice, has much greater coverage of algorithms for two or more non-periodic directions, and shows how to treat outflow boundaries. Material on spectral methods for compressible flow emphasizes boundary conditions for hyperbolic systems, algorithms for simulation of homogeneous turbulence, and improved methods for shock fitting. This book is a companion to Spectral Methods: Fundamentals in Single Domains.

Evolution to Complex Geometries and Applications to Fluid Dynamics

Spectral Methods

Anita Tabacco

The recen t Europea n Programm e Specification s hav e force d a reassessmen t o f th e structure an d syllab i o f th e entir e syste m o f Italia n highe r education , an d a n ensuing rethinkin g o f th e teachin g material . Nowadays man y lectur e courses , especiall y rudimentar y ones , deman d tha t st- dents maste r a larg e amoun t o f theoretica l an d practica l knowledg e i n a spa n o f just fe w weeks , i n orde r t o gai n a smal l numbe r o f credits . A s a result , instructor s face th e dilemm a o f ho w t o presen t th e subjec t matter . The y mus t mak e appr- priate choice s abou t lectur e content , th e comprehensio n leve l require d fro m th e recipients, an d whic h kin d o f languag e t o use .

Mathematical Analysis I

The purpose of the volume is to provide a support for a first course in Mathematics. The contents are organised to appeal especially to Engineering, Physics and Computer Science students, all areas in which mathematical tools play a crucial role. Basic notions and methods of differential and integral calculus for functions of one real variable are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The layout has a specifically-designed modular nature, allowing the instructor to make flexible didactical choices when planning an introductory lecture course. The book may in fact be employed at three levels of depth. At the elementary level the student is supposed to grasp the very essential ideas and familiarise with the corresponding key techniques. Proofs to the main results befit the intermediate level, together with several remarks and complementary notes enhancing the treatise. The last, and farthest-reaching, level requires the additional study of the material contained in the appendices, which enable the strongly motivated reader to explore further into the subject. Definitions and properties are furnished with substantial examples to stimulate the learning process. Over 350 solved exercises complete the text, at least half of which guide the reader to the solution. This new edition features additional material with the aim of matching the widest range of educational choices for a first course of Mathematics.

Since the publication of "Spectral Methods in Fluid Dynamics" 1988, spectral methods have become firmly established as a mainstream tool for scientific and engineering computation. The authors of that book have incorporated into this new edition the many improvements in the algorithms and the theory of spectral methods that have been made since then. This latest book retains the tight integration between the theoretical and practical aspects of spectral methods, and the chapters are enhanced with material on the Galerkin with numerical integration version of spectral methods. The discussion of direct and iterative solution methods is also greatly expanded.

Fundamentals in Single Domains

The purpose of the volume is to provide a support textbook for a second lecture course on Mathematical Analysis. The contents are organised to suit, in particular, students of Engineering, Computer Science and Physics, all areas in which mathematical tools play a crucial role. The basic notions and methods concerning integral and differential calculus for multivariable functions, series of functions and ordinary differential equations are presented in a manner that elicits critical reading and prompts a hands-on approach to concrete applications. The pedagogical layout echoes the one used in the companion text Mathematical Analysis I. The book’s structure has a specifically-designed modular nature, which allows for great flexibility in the preparation of a lecture course on Mathematical Analysis. The style privileges clarity in the exposition and a linear progression through the theory. The material is organised on two levels. The first, reflected in this book, allows students to grasp the essential ideas, familiarise with the corresponding key techniques and find the proofs of the main results. The second level enables the strongly motivated reader to explore further into the subject, by studying also the material contained in the appendices. Definitions are enriched by many examples, which illustrate the properties discussed. A host of solved exercises complete the text, at least half of which guide the reader to the solution. This new edition features additional material with the aim of matching the widest range of educational choices for a second course of Mathematical Analysis.

Mathematical Analysis II

Il testo intende essere di supporto ad un primo insegnamento di Analisi Matematica secondo i principi dei nuovi Ordinamenti Didattici. È in particolare pensato per Ingegneria, Informatica, Fisica. Il testo presenta tre diversi livelli di lettura. Un livello essenziale permette allo studente di cogliere i concetti indispensabili della materia e di familiarizzarsi con le relative tecniche di calcolo. Un livello intermedio fornisce le giustificazioni dei principali risultati e arricchisce l'esposizione mediante utili osservazioni e complementi. Un terzo livello di lettura, basato su numerosi riferimenti ad un testo virtuale disponibile in rete, permette all'allievo più motivato ed interessato di approfondire la sua preparazione sulla materia. Completano il testo numerosi esempi ed esercizi con soluzioni. La grafica accattivante, a 2 colori, fa di questo testo un punto di riferimento fondamentale per lo studio della disciplina.

Claudio Canuto

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