Introduction to Scientific Computing

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.Die meisten ingenieurtechnischen und physikalischen Probleme lassen sich durch numerische Analyse mit Hilfe partieller Differentialgleichungen lösen. In diesem Buch werden Methoden zur Lösung von partiellen Differentialgleichungssystemen behandelt. Die Autoren zeigen anhand zahlreicher Beispiele Wege zur Programmierung solcher Fragestellungen unter Verwendung finiter Elemente. Spezielle Kapitel beschäftigen sich ausführlich mit numerischen Methoden, Algorithmen für Parallelrechentechnik und Mehrprozessorsystemen. (12/97) 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. PART A: PROGRAMMING THE MODEL PROBLEM BY A FINITE ELEMENT METHOD;
Introduction to the Finite Element Method ;
Energy Minimization;
Finite Element Method: Variational Formulation and Direct Methods;
Finite Element Method: Optimization of the Method;
PART B: 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 for Time Variable;
Integral Methods for the Laplacian;
Some Algorithms for Parallel Computing;
Bibliography;
Index.

Brigitte Lucquin is the author of Introduction to Scientific Computing, published by Wiley. Olivier Pironneau is a French mathematician who is a Professor at the Université Pierre et Marie Curie and member of the French Academy of Sciences.
Pironneau is a worldwide recognized expert in computational fluid dynamics, scientific computing, optimal design, numerical analysis and partial differential equations. 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.