An Introduction to Scientific Computing

Ionut Danaila is Professor of Applied Mathematics at the University of Rouen Normandy, Laboratoire de mathématiques Raphaël Salem, and former member of Laboratoire  Jacques-Louis Lions, Sorbonne Université. He is co-author of  two textbooks (in French) on scientific computing and one research monograph (on vortex ring models) for researchers and graduate students. His main research interests are in numerical analysis and modern scientific computing. He developed several numerical codes for applications in fluid mechanics, quantum physics and thermal sciences. Over the last decade, he headed two fundamental research projects on the mathematical modelling and high-performance simulation of quantum systems (Bose-Einstein condensates and superfluid helium). Pascal Joly, now retired, was Research Scientist at Laboratoire  Jacques-Louis Lions, Sorbonne Université and Centre national de la recherche scientifique (CNRS). His main research interests concern efficient algorithms in scientific computing (such as solving large sparse linear systems of equations), coding finite element methods for various industrial applications and exploring the wavelets theory in signal processing. He taught courses on numerical methods in various engineering schools and he is former deputy director of the Master of Sciences and Technology of the Université Pierre et Marie Curie for applied Mathematics.   Sidi-Mahmoud Kaber is Associate Professor of Applied Mathematics at Laboratoire  Jacques-Louis Lions, Sorbonne Université. He is co-author of three textbooks in French and one in English on numerical analysis. His main research interests include approximation of singular functions and numerical schemes for parallel computing. He is very engaged in using programming and software in mathematics education.     Marie Postel is Associate Professor of Applied Mathematics at Laboratoire  Jacques-Louis Lions, Sorbonne Université. She is co-author of two textbooks (in French) on numerical methods. Her research interests are currently mathematical modeling of biological systems, along with the numerical simulation and calibration of model using experimental data. She has designed several adaptive methods in scientific computing for PDEs using multiresolution analysis. She is currently the head of a master program in engineering mathematics, and teaches numerical methods for ODEs, PDEs and optimization at undergraduate and graduate level.  

Numerical Approximation of Model Partial Differential Equations.- Nonlinear Differential Equations: Application to Chemical Kinetics.- Polynomial Approximation.- Solving an Advection-Diffusion Equation by a Finite Element Method.- Solving a Differential Equation by a Spectral Method.- Signal Processing: Multiresolution Analysis.- Elasticity: Elastic Deformation of a Thin Plate.- Domain Decomposition Using a Schwarz Method.- Geometrical Design: Bézier Curves and Surfaces.- Gas Dynamics: The Riemann Problem and Discontinuous Solutions: Application to the Shock Tube Problem.- Thermal Engineering: Optimization of an Industrial Furnace.- Fluid Dynamics: Solving the Two-Dimensional Navier-Stokes Equations.