Numerical and Symbolic Scientific Computing

1. Front Matter

   Pages i-viii

   PDF

2. Approximate Implicitization of Space Curves

   • Martin Aigner, Bert Jüttler, Adrien Poteaux

   Pages 1-19

3. Sparsity Optimized High Order Finite Element Functions on Simplices

   • Sven Beuchler, Veronika Pillwein, Joachim Schöberl, Sabine Zaglmayr

   Pages 21-44

4. Fast Solvers and A Posteriori Error Estimates in Elastoplasticity

   • Peter G. Gruber, Johanna Kienesberger, Ulrich Langer, Joachim Schöberl, Jan Valdman

   Pages 45-63

5. A Symbolic-Numeric Algorithm for Genus Computation

   • Mădălina Hodorog, Josef Schicho

   Pages 65-94

6. The “Seven Dwarfs” of Symbolic Computation

   • Erich L. Kaltofen

   Pages 95-104

7. Computer Algebra Meets Finite Elements: An Efficient Implementation for Maxwell’s Equations

   • Christoph Koutschan, Christoph Lehrenfeld, Joachim Schöberl

   Pages 105-121

8. A Symbolic Approach to Generation and Analysis of Finite Difference Schemes of Partial Differential Equations

   • Viktor Levandovskyy, Bernd Martin

   Pages 123-156

9. White Noise Analysis for Stochastic Partial Differential Equations

   • Hermann G. Matthies

   Pages 157-174

10. Smoothing Analysis of an All-at-Once Multigrid Approach for Optimal Control Problems Using Symbolic Computation

    • Stefan Takacs, Veronika Pillwein

    Pages 175-191

11. Analytical Evaluations of Double Integral Expressions Related to Total Variation

    • Carsten Pontow, Otmar Scherzer

    Pages 193-218

12. Sound and Complete Verification Condition Generator for Functional Recursive Programs

    • Nikolaj Popov, Tudor Jebelean

    Pages 219-256

13. An Introduction to Automated Discovery in Geometry through Symbolic Computation

    • Tomas Recio, María P. Vélez

    Pages 257-271

14. Symbolic Analysis for Boundary Problems: From Rewriting to Parametrized Gröbner Bases

    • Markus Rosenkranz, Georg Regensburger, Loredana Tec, Bruno Buchberger

    Pages 273-331

15. Linear Partial Differential Equations and Linear Partial Differential Operators in Computer Algebra

    • Ekaterina Shemyakova, Franz Winkler

    Pages 333-358

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.

• applied geometry
• computational mathematics
• numerical analysis
• scientific computing
• symbolic computation

• Inst. Numerische Mathematik, Universität Linz, Linz, Austria

  Ulrich Langer

• , Research Institute for Symbolic Computat, Johannes Kepler University, Linz, Austria

  Peter Paule

Policies and ethics