Böcker av Ionut Danaila

This book demonstrates scientific computing by presenting twelve computational projects spanning a broad spectrum of disciplines including Fluid Mechanics, Chemistry, Elasticity, Thermal Science, Computer Aided Design, Signal and Image Processing and more. Each project guides the reader through typical steps of scientific computing, from physical and mathematical description of the problem, to numerical formulation and programming and finally to critical discussion of results. The text teaches practical computational methods which are not usually available in basic textbooks: numerical checking of accuracy or stability, choice of boundary conditions, effective solving of linear systems, comparison to exact solutions and more. Programming techniques such as vectorial programming and memory storage optimization are addressed, and chapter-ending references form a guide for further reading. The final section of each project contains the solutions to proposed exercises and guides the reader in using the MATLAB scripts available online.

The Institute for Mathematical Sciences at the National University of Singapore hosted a thematic program on Quantum and Kinetic Problems: Modeling, Analysis, Numerics and Applications from September 2019 to March 2020. As an important part of the program, tutorials and special lectures were given by leading experts in the fields for participating graduate students and junior researchers.This invaluable volume collects six expanded lecture notes with self-contained tutorials. The coverage includes mathematical models and numerical methods for multidimensional solitons in linear and nonlinear potentials; Bose-Einstein condensation (BEC) with dipole-dipole interaction, higher order interaction and spin-orbit coupling; classical and quantum turbulence; and molecular dynamics process based on the first-principle in quantum chemistry.This volume serves to inspire graduate students and researchers who will embark into original research work in these fields.