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Introduction to Scientific Computing [Pehme köide]

(Sorbonne University Pierre and Marie Curie Campus, France), (Sorbonne University Pierre and Marie Curie Campus, France)
  • Formaat: Paperback / softback, 380 pages, kõrgus x laius x paksus: 243x172x22 mm, kaal: 680 g
  • Ilmumisaeg: 29-Jan-1998
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 0471972665
  • ISBN-13: 9780471972662
Teised raamatud teemal:
Introduction to Scientific ComputingSuurem pilt
  • Formaat: Paperback / softback, 380 pages, kõrgus x laius x paksus: 243x172x22 mm, kaal: 680 g
  • Ilmumisaeg: 29-Jan-1998
  • Kirjastus: John Wiley & Sons Inc
  • ISBN-10: 0471972665
  • ISBN-13: 9780471972662
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780471972662.html
Märksõnad:
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.
Foreword ix(2)
Introduction xi
1 Some Partial Differential Equations
1(26)
1.1 Membranes
1(2)
1.2 Electrostatic
3(1)
1.3 Thermal Conduction
4(5)
1.4 Acoustics
9(1)
1.5 Irrotational Flow
10(3)
1.6 Convection
13(4)
1.7 Navier-Stokes Equations
17(1)
1.8 Examples with Systems
18(4)
1.9 An Examples with Complex Numbers
22(2)
1.10 Classification of the Equations
24(3)
PART A PROGRAMMING THE MODEL PROBLEM BY A FINITE ELEMENT METHOD 27(144)
2 Introduction to the Finite Element Method; Energy Minimisation
27(60)
2.1 Statement of the Problem
27(4)
2.2 Transformation of the Problem
31(3)
2.3 Approximation by the Galerkin Method
34(4)
2.4 First order Finite Elements: Triangulation, Interpolation, Quadrature Formulae
38(9)
2.5 Programming the Method
47(19)
2.6 Efficiency of the Method
66(7)
2.A Appendix: The Complete Fortran Program for Solving the Laplace Equation with Dirichlet Boundary Conditions by Energy Minimisation
73(8)
2.B Appendix: The Complete Program, in C Language, for Solving the Laplace Equation with Dirichlet Boundary Conditions by Energy Minimisation
80(7)
3 Finite Element Method: Variational Formulation and Direct Methods
87(52)
3.1 Statement of the Problem
87(2)
3.2 Solving the Discrete Variational Formulation by Band Storage of the Matrix
89(14)
3.3 Numbering of Edges and Neighbouring Points
103(9)
3.4 Compressed Sparse Row Storage
112(11)
3.5 Efficiency of the Method
123(1)
3.A Appendix: The Fortran Program for Solving the Laplacian with Dirichlet Boundary Conditions by Variational Formulation and Choleski Factorisation of the Linear System Matrix Stored in Band Format
123(5)
3.B Appendix: The Fortran Program for Solving the Laplacian with Dirichlet Boundary Conditions by Variational Formulation and Choleski Factorisation of the Linear System Matrix, stored in CSR format
128(11)
4 Finite Element Method: Optimisation of the Method
139(32)
4.1 Preconditioned Conjugate Gradient
139(9)
4.2 Programming the Method
148(4)
4.3 Application to the Laplace Equation
152(1)
4.4 Automatic Mesh Refinement
153(6)
4.5 Delaunay Triangulation
159(3)
4.A Appendix: Proof of Lemma 4.1 and Propositions 4.3 and 4.6
162(2)
4.B Appendix: The Fortran Program for Solving the Laplacion and Dirichlet Boundary Conditions by a Variational Formulation and Resolution of the Linear Systems by Conjugate Gradient Preconditioned by the Incomplete Choleski Factorisation of the System Matrix
164(7)
PART B GENERAL ELLIPTIC PROBLEMS AND EVOLUTION PROBLEMS 171(138)
5 Finite Element Method for General Elliptic Problems
171(44)
5.1 Neumann or Robin Boundary Conditions
171(8)
5.2 General Symmetric and Linear Elliptic Equations
179(11)
5.3 Second Order Finite Elements
190(9)
5.4 Second Order Systems
199(2)
5.A Appendix: The Fortran Program for the Solution of a Partial Differential Equation with Very General Boundary Condition by Conjugate Gradient Preconditioned by the Diagonal
201(14)
6 Non-symmetric or Non-linear Partial Differential Equations
215(34)
6.1 Second Order Non-symmetric Problems
215(4)
6.2 The GMRES algorithm
219(10)
6.3 One Example of a Non-linear Problem
229(5)
6.A Appendix: The Fortran Subroutine for Solving a Linear System with an Invertible, but not Necessarily Symmetric Matrix A, by the Linear GMRES(m) Algorithm
234(5)
6.B Appendix: The C Program for Solving a Linear Non-symmetric PDE by Gauss factorisation of the Linear System
239(10)
7 Evolution Problems: Finite Differences in Time
249(60)
7.1 The Finite Difference Method
249(9)
7.2 Finite Difference Schemes for Linear Evolution Problems
258(4)
7.3 The Heat Equation
262(25)
7.4 The Convection Equation
287(5)
7.5 The Convection-Diffusion Equation
292(3)
7.6 The Wave Equation
295(3)
7.7 Finite Differences in Time and Finite Elements in Space
298(2)
7.8 Finite Differences in Time and Finite Volumes in Space
300(4)
7.A Appendix: The Fortran Program for Solving the Heat Equation with Homogeneous Dirichlet Boundary Condition by Two Different Schemes in Time: the Explicit Scheme, and the Implicit Scheme
304(5)
PART C COMPLEMENTS ON NUMERICAL METHODS 309(46)
8 Integral Methods for the Laplacian
309(24)
8.1 Preliminaries
309(8)
8.2 Solution of the Dirichlet Problem by a Single Layer Potential
317(9)
8.3 Other Problems
326(7)
9 Some Algorithms for Parallel Computing
333(22)
9.1 Architectures and Performances
333(1)
9.2 Parallelism
334(2)
9.3 Subdomain Parallelisation
336(6)
9.4 The Schur Complement Method
342(4)
9.5 A Lagrangian Method
346(1)
9.6 Mortar Elements
347(4)
9.7 Perspectives
351(1)
9.A Appendix: Conditions Number of the Schur Matrix
351(4)
Bibliography 355(4)
Index 359


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.