Overview
- Offers a survey of post-Newtonian computations for black-hole spacetimes after gravitational wave observation
- Addresses numerical algorithms for hyperbolic systems and 2D drift-diffusion equations without dimensional splitting
- Presents application of hyperbolic systems of balance laws to global isometric immersions of 2d Riemann surfaces
Part of the book series: Springer INdAM Series (SINDAMS, volume 16)
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Table of contents (12 chapters)
Keywords
- Numerial analysis of non-local drift-diffusion equations
- Preliminary computations of 2d non-standard solutions
- Post-Newtonian computations in black-hole spacetimes
- Filtering for inverse design problems of Burgers equation
- Semi-analytical methods for sound waves in rarefied gas
- partial differential equations
About this book
This volume gathers contributions reflecting topics presented during an INDAM workshop held in Rome in May 2016. The event brought together many prominent researchers in both Mathematical Analysis and Numerical Computing, the goal being to promote interdisciplinary collaborations. Accordingly, the following thematic areas were developed:
1. Lagrangian discretizations and wavefront tracking for synchronization models;
2. Astrophysics computations and post-Newtonian approximations;
3. Hyperbolic balance laws and corrugated isometric embeddings;
4. “Caseology” techniques for kinetic equations;
5. Tentative computations of compressible non-standard solutions;
6. Entropy dissipation, convergence rates and inverse design issues.
Most of the articles are presented in a self-contained manner; some highlight new achievements, while others offer snapshots of the “state of the art” in certain fields. The book offers a unique resource, both for young researchers looking to quickly enter a given area of application, and for more experienced ones seeking comprehensive overviews and extensive bibliographic references.
Editors and Affiliations
About the editors
Laurent Gosse received the M.S. and Ph.D. degrees both in Mathematics from Universities of Lille 1 and Paris IX Dauphine in 1991 and 1997 respectively. Between 1997 and 1999 he was a TMR postdoc in IACM-FORTH (Heraklion, Crete) mostly working on well-balanced numerical schemes and a posteriori error estimates with Ch. Makridakis. From 1999 to 2001, he was postdoc in Universtity of L'Aquila (Italy) working on stability theory for systems of balance laws and multiphase computations in geometrical optics with K-multibranch solutions. In 2001, he moved to University of Pavia working on asymptotic-preserving schemes and degenerate parabolic equations with G. Toscani. In 2002, he was granted a permanent researcher position at CNR in Bari (Italy) where he developed Lagrangian schemes for nonlinear diffusion models and a stable inversion algorithm for Markov moment problem with O. Runborg. Numerical investigation of semiclassical WKB approximation for quantum models of crystals was conducted with P.A. Markowich between 2003 and 2006. Since 2011, he holds a CNR position at both Roma and University of L'Aquila and works mainly on the applications of Caseology to well-balanced schemes for collisional kinetic equations.
Roberto Natalini received his PhD in Mathematics from the University of Bordeaux I (France) in 1986. He has been the Director of the National Research Council of Italy’s Istituto per le Applicazioni del Calcolo since 2014. His research interests include: analysis of hyperbolic systems of conservation laws, fluid dynamics, road traffic, semiconductors, chemical damage to monuments, and biomathematics. He serves on the Board of the Italian Society of Industrial and Applied Mathematics and is Chair of the European Mathematical Society’s Raising Awareness Committee.
Bibliographic Information
Book Title: Innovative Algorithms and Analysis
Editors: Laurent Gosse, Roberto Natalini
Series Title: Springer INdAM Series
DOI: https://doi.org/10.1007/978-3-319-49262-9
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-49261-2Published: 17 March 2017
Softcover ISBN: 978-3-319-84117-5Published: 20 July 2018
eBook ISBN: 978-3-319-49262-9Published: 26 May 2016
Series ISSN: 2281-518X
Series E-ISSN: 2281-5198
Edition Number: 1
Number of Pages: XVIII, 351
Number of Illustrations: 10 b/w illustrations, 60 illustrations in colour
Topics: Applications of Mathematics, Partial Differential Equations, Computational Mathematics and Numerical Analysis, Mathematical and Computational Biology, Differential Geometry, Mathematical Methods in Physics