Computational Partial Differential Equations: Numerical Methods and Diffpack Programming
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. 7. 6), - a solver for vibration of elastic structures (Chapter 5. 1. 6), - a step-by-step instruction of how to develop and test Diffpack programs for a physical application (Chapters 3. 6 and 3. 13), - construction of non-trivial grids using super elements (Chapters 3. 5. 4, 3. 6. 4, and 3. 13. 4), - additional material on local mesh refinements (Chapter 3. 7), - coupling of Diffpack with other types of software (Appendix B. 3) - high-level programming offinite difference solvers utilizing the new stencil (finite difference operator) concept in Diffpack (Appendix D. 8). 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. 2. Errors have been corrected, many explanations have been extended, and the text has been upgraded to be compatible with Diffpack version 4. 0. 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.
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Introduction to Finite Element Discretization
Programming of Finite Element Solvers 251
Solid Mechanics Applications
A Mathematical Topics
B Diffpack Topics
Iterative Methods for Sparse Linear Systems
Software Tools for Solving Linear Systems
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Computational Partial Differential Equations: Numerical Methods and Diffpack ...
Hans Petter Langtangen
No preview available - 2014
algorithm analytical solution apply approximation array ArrayGen base class basis functions boundary conditions boundary indicators casename Chapter coefficient command command-line compute constant convergence Courant number curve curveplot default define derivatives differential equation Diffpack discrete equations domain elmat error essential boundary example Exercise field finite difference method finite element method flux formulation Galerkin Galerkin method Gaussian elimination global gnuplot grid points Handle heat equation implementation initial condition input file integrands interface iteration linear elements linear system loop mathematical Matlab menu items menu system mesh model problem MyVector nodes nonlinear norm numerical object option parameters plot Plotmtv Poisson2 preprocessor Python quadratic refinement scan script simres simulator solve solveProblem solver source code sparse matrix string subclass super element syntax term time-dependent tstop values variable vector velocity virtual function virtual void visualization wave equation weighted residual