Introduction to Scientific Computing

ISBN-13: 9780471972662 / Angielski / Miękka / 1998 / 380 str.

Brigitte Lucquin; Olivier Pironneau; B. Lucquin

Opis

This volume addresses the methods for solving partial differential equations (PDE) systems. The reader should learn how to write computer programs for the numerical analysis of practical engineering problems. Illustrated by examples, it starts by the definition of a programming environment for the solving of PDE systems by the finite element method. Programming the model problem by a finite element method is then addressed in detail. General elliptic problems and evolution problems are then dealt with. Finally, complements on numerical methods, algorithms for parallel computing and multiprocessor computers are presented.

Spis treści

Some Partial Differential Equations.

PROGRAMMING THE MODEL PROBLEM BY A FINITE ELEMENT METHOD.

Introduction to the Finite Element Method: Energy Minimisation.

Finite Element Method: Variational Formulation and Direct Methods.

Finite Element Method: Optimisation of the Method.

GENERAL ELLIPTIC PROBLEMS AND EVOLUTION PROBLEMS.

Finite Element Method for General Elliptic Problems.

Non–symmetric or Non–linear Partial Differential Equations.

Evolution Problems: Finite Differences in Time.

COMPLEMENTS ON NUMERICAL METHODS.

Integral Methods for the Laplacian.

Some Algorithms for Parallel Computing.

Bibliography.

Index.

Blurb

This book presents the basic scientific computing methods for the solution of partial differential equations (PDEs) as they occur in engineering problems. Programming codes in Fortran and C are included for each problem. Opening with the definition of the programming environment for the solving of PDE systems, it then addresses in detail the programming of the model problem by the finite element method. Efficiency, compact storage pre–conditioning and mesh adaption are also presented. General elliptic problems and evolution problems are then dealt with. Finally, topics related to other numerical methods, algorithms for parallel computing and multi processor computers are detailed. An integrated software package which illustrates the featured programs of PDEs is available on the Internet via anonymous FTP. The methods presented have applications in numerous fields of engineering including shape optimisation, nuclear safety, heat transfer, acoustics, mechanics of fluids and elasticity, and are also relevant to other areas such as pollution, meteorology, biology, etc.