It seems that you're in Germany. We have a dedicated site for Germany. Experimentation based on numerical simulation has become fundamental in engineering and many of the traditional sciences. This text aims at equipping the reader with tools and skills for formulating solution methods for PDEs and producing associated running code.
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Hans Petter Langtangen. The second edition features lots of improvements and new material. The most significant additions include - finite difference methods and implementations for a 1D time-dependent heat equation Chapter 1. Many of the examples, projects, and exercises from the first edition have been revised and improved. Some new exercises and projects have also been added. A hopefully very useful new feature is the compact overview of all the program examples in the book and the associated software files, presented in Chapter 1.
Errors have been corrected, many explanations have been extended, and the text has been upgraded to be compatible with Diffpack version 4. The major difficulty when developing programs for numerical solution of partial differential equations is to debug and verify the implementation. This requires an interplay between understanding the mathematical model,the in volved numerics, and the programming tools. Introduction to Finite Element Discretization.
A ID Poisson Equation. A ID Wave Equation. A 2D Wave Equation. Programming of Finite Element Solvers. CornerFlow Singularity. Nonlinear Problems. Solid Mechanics Applications. Fluid Mechanics Applications. Coupled Problems. A2 Indicial Notation.
A 3 Compact Notation for Difference Equations. A4 Stability and Accuracy of Difference Approximations. A42 Physical Significance of Parameters in the Solution. A43 Analytical Dispersion Relations.
A44 Solution of Discrete Equations. A45 Numerical Dispersion Relations. A49 Truncation Error. A Traditional von Neumann Stability Analysis. Analysis of the Heat Equation. A52 An Elliptic Equation. A55 WellPosed Problems. B41 Diffpack Man Pages. B42 Standard CommandLine Options. B43 Generalized Input and Output. B 14 Automatic Verification of a Code. B5 Visualization Support. B52 Scalar and Vector Fields. B62 Using Functors for the Integrands.
B63 Integrating Quantities over the Grid or the Boundary. B7 Optimizing Diffpack Codes. B71 Avoiding Repeated Matrix Factorizations. B73 Optimizing the Assembly Process. B74 Optimizing Array Indexing. Iterative Methods for Sparse Linear Systems. CI Classical Iterative Methods.
C11 A General Framework. C21 Galerkin and LeastSquares Methods. C22 Summary of the Algorithms. C23 A Framework Based on the Error. C31 Motivation and Basic Principles. C32 Classical Iterative Methods as Preconditioners. C33 Incomplete Factorization Preconditioners. C4 Multigrid and Domain Decomposition Methods. C41 Domain Decomposition. C42 Multigrid Methods. Software Tools for Solving Linear Systems. D12 Detailed Matrix Examples.
D13 Representation of Linear Systems. D2 Programming with Linear Solvers. D22 A Simple Demo Program. D3 Classical Iterative Methods. D4 Conjugate Gradientlike Methods. D 12 Nonsymmetric Systems. D5 Preconditioning Strategies. D6 Convergence History and Stopping Criteria. Implicit Methods for Transient Diffusion. D83 Defining the Stencils. Hans P. Elias N. Houstis , John R.
Getting Started. A46 Convergence. A47 Stability. A48 Accuracy. B21 Unix. B22 Windows. B51 Curves.
Computational Partial Differential Equations : Numerical Methods and Diffpack Programming
Computational Partial Differential Equations
Hans P. The second edition features lots of improvements and new material. The most significant additions include - finite difference methods and implementations for a 1D time-dependent heat equation Chapter 1. Many of the examples, projects, and exercises from the first edition have been revised and improved. Some new exercises and projects have also been added. A hopefully very useful new feature is the compact overview of all the program examples in the book and the associated software files, presented in Chapter 1.