Numerical and Symbolic Scientific Computing: Progress and Prospects

✍ Scribed by Martin Aigner, Bert Jüttler, Adrien Poteaux (auth.), Ulrich Langer, Peter Paule (eds.)

• Publisher: Springer-Verlag Wien
• Year: 2012
• Tongue: English
• Leaves: 360
• Series: Texts & Monographs in Symbolic Computation
• Edition: 1
• Category: Library

✦ Synopsis

The book presents the state of the art and results and also includes articles pointing to future developments. Most of the articles center around the theme of linear partial differential equations. Major aspects are fast solvers in elastoplasticity, symbolic analysis for boundary problems, symbolic treatment of operators, computer algebra, and finite element methods, a symbolic approach to finite difference schemes, cylindrical algebraic decomposition and local Fourier analysis, and white noise analysis for stochastic partial differential equations. Further numerical-symbolic topics range from applied and computational geometry to computer algebra methods used for total variation energy minimization.

✦ Table of Contents

Front Matter....Pages i-viii
Approximate Implicitization of Space Curves....Pages 1-19
Sparsity Optimized High Order Finite Element Functions on Simplices....Pages 21-44
Fast Solvers and A Posteriori Error Estimates in Elastoplasticity....Pages 45-63
A Symbolic-Numeric Algorithm for Genus Computation....Pages 65-94
The “Seven Dwarfs” of Symbolic Computation....Pages 95-104
Computer Algebra Meets Finite Elements: An Efficient Implementation for Maxwell’s Equations....Pages 105-121
A Symbolic Approach to Generation and Analysis of Finite Difference Schemes of Partial Differential Equations....Pages 123-156
White Noise Analysis for Stochastic Partial Differential Equations....Pages 157-174
Smoothing Analysis of an All-at-Once Multigrid Approach for Optimal Control Problems Using Symbolic Computation....Pages 175-191
Analytical Evaluations of Double Integral Expressions Related to Total Variation....Pages 193-218
Sound and Complete Verification Condition Generator for Functional Recursive Programs....Pages 219-256
An Introduction to Automated Discovery in Geometry through Symbolic Computation....Pages 257-271
Symbolic Analysis for Boundary Problems: From Rewriting to Parametrized Gröbner Bases....Pages 273-331
Linear Partial Differential Equations and Linear Partial Differential Operators in Computer Algebra....Pages 333-358

✦ Subjects

Computational Mathematics and Numerical Analysis; Algebra; Appl.Mathematics/Computational Methods of Engineering