The increasing role of artificial intelligence to automate decision-making sparks concern about potential AI-based discrimination.
Matrices of small integers—innocuous as they may seem—can clearly provoke interesting behavior.
Joseph Teran spoke about the use of mathematical models for computer-generated imagery at AN18.
Gil Strang identifies continuous piecewise linear functions as powerful approximators in an effort to transform shallow learning into deep learning.
On the occasion of a birthday celebration, Walter Gautschi describes his interest in different research areas.
Nature can overcome the second law of thermodynamics and (nearly) exchange the temperatures of two substances.
Per-Gunnar Martinsson describes two randomized algorithms designed to help process large datasets in high-dimensional spaces.
2018 / xvi + 570 pages / softcover / ISBN 978-1-611975-09-3 / List Price $89.00 / SIAM Member Price $62.30 / Order Code: CS18
Keywords: conservation laws, monotone schemes, high-order methods, WENO/ENO methods, discontinuous Galerkin methids, spectral methods
Conservation laws are the mathematical expression of the principles of conservation and provide effective and accurate predictive models of our physical world. Although intense research activity during the last decades has led to substantial advances in the development of powerful computational methods for conservation laws, their solution remains a challenge and many questions are left open; thus it is an active and fruitful area of research.
Numerical Methods for Conservation Laws: From Analysis to Algorithms
Code and other supplemental material will be available online at publication.
This book is intended for graduate students in computational mathematics and researchers seeking a comprehensive introduction to modern methods for solving conservation laws. Students and researchers in applied sciences and engineering will benefit from the book’s emphasis on algorithmic aspects of complex algorithms. The text also includes extensive references which allows researchers to pursue advanced research and results.
About the Author
Jan S. Hesthaven is Dean of Basic Sciences, Professor of Mathematics, and holds the Chair of Computational Mathematics and Simulation Science at Ecole Polytechnique Fédérale de Lausanne (EPFL) in Switzerland. Prior to joining EPFL in 2013, he was Professor of Applied Mathematics at Brown University. He has worked for more than two decades on the development, analysis, and application of modern computational methods for linear and nonlinear wave problems, with an emphasis on high-order accurate methods. He is an Alfred P. Sloan Fellow (2001), an NSF Career award winner (2002), and a SIAM Fellow (2014).
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