Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

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The target audience of this book is students and researchers in computational sciences who need to develop computer codes for solving partial differential equations. The exposition is focused on numerics and software related to mathematical models in solid and fluid mechanics. The book teaches finite element methods and basic finite difference methods from a computational point of view. The main emphasis regards development of flexible computer programs, using the numerical library Diffpack. The application of ...
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1999 Hard cover New. No dust jacket. Sewn binding. Cloth over boards. 682 p. Lecture Notes in Computational Science and Engineering, 2. Audience: General/trade. *****PLEASE ... NOTE: This item is shipping from an authorized seller in Europe. In the event that a return is necessary, you will be able to return your item within the US. To learn more about our European sellers and policies see the BookQuest FAQ section***** Read more Show Less

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Overview

The target audience of this book is students and researchers in computational sciences who need to develop computer codes for solving partial differential equations. The exposition is focused on numerics and software related to mathematical models in solid and fluid mechanics. The book teaches finite element methods and basic finite difference methods from a computational point of view. The main emphasis regards development of flexible computer programs, using the numerical library Diffpack. The application of Diffpack is explained in detail for problems including model equations in applied mathematics, heat transfer, elasticity, and viscous fluid flow. Diffpack is a modern software development environment based on C++ and object-oriented programming.
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Product Details

Table of Contents

1 Getting Started 1
1.1 The First Diffpack Encounter 3
1.2 Overview of Application Examples 7
1.3 Steady One-Dimensional Heat Conduction 12
1.4 Simulation of Waves 32
1.5 Projects 62
1.6 About Programming with Objects 65
1.7 Coding the PDE Simulator as a Class 101
1.8 Projects 131
2 Introduction to Finite Element Discretization 141
2.1 Weighted Residual Methods 142
2.2 Time Dependent Problems 152
2.3 Finite Elements in One Space Dimension 157
2.4 Example: A 1D Wave Equation 176
2.5 Naive Implementation 183
2.6 Projects 189
2.7 Higher-Dimensional Finite Elements 195
2.8 Calculation of Derivatives 206
2.9 Convection-Diffusion Equations 212
2.10 Analysis of the Finite Element Method 220
3 Programming of Finite Element Solvers 251
3.1 A Simple Programs for the Poisson Equation 252
3.2 Increasing the Flexibility 261
3.3 Some Visualization Tools 268
3.4 Some Useful Diffpack Features 281
3.5 Introducing More Flexibility 295
3.6 Step-by-Step Development of a Diffpack Solver 335
3.7 Adaptive Grids 362
3.8 Projects 380
3.9 A Convection-Diffusion Solver 387
3.10 A Heat Equation Solver 391
3.11 A More Flexible Heat Equation Solver 398
3.12 Visualization of Time-Dependent Fields 402
3.13 A Transient Heat Transfer Application 417
3.14 Projects 443
3.15 Efficient Solution of the Wave Equation 447
4 Nonlinear Problems 459
4.1 Discretization and Solution of Nonlinear PDEs 459
4.2 Software Tools for Nonlinear Finite Element Problems 477
4.3 Projects 487
5 Solid Mechanics Applications 493
5.1 Linear Thermo-Elasticity 494
5.2 Elasto-Viscoplasticity 522
6 Fluid Mechanics Applications 539
6.1 Convection-Diffusion Equations 539
6.2 Shallow Water Equations 546
6.3 An Implicit Finite Element Navier-Stokes Solver 562
6.4 A Classical Finite Difference Navier-Stokes Solver 576
6.5 A Fast Finite Element Navier-Stokes Solver 586
6.6 Projects 591
7 Coupled Problems 595
7.1 Fluid-Structure Interaction; Squeeze-Film Damping 595
7.2 Fluid Flow and Heat Conduction in Pipes 611
7.3 Projects 626
A Mathematical Topics 633
B Diffpack Topics 681
C Iterative Methods for Sparse Linear Systems 751
D Software Tools for Solving Linear Systems 781
Bibliography 833
Index 843
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