Introduction to High Performance Scientific Computing

Scientific computing is the cross-disciplinary field at the intersection of modeling scientific processes, and the use of computers to produce quantitative results from these models. It is what takes a domain science and turns it into a computational activity. As a definition, we may posit The efficient computation of constructive methods in applied mathematics.

This clearly indicates the three branches of science that scientific computing touches on:

• Applied mathematics: the mathematical modeling of real-world phenomena. Such modeling often leads to implicit descriptions, for instance in the form of partial differential equations. In order to obtain actual tangible results we need a constructive approach.
• Numerical analysis provides algorithmic thinking about scientific models. It offers a constructive approach to solving the implicit models, with an analysis of cost and stability.
• Computing takes numerical algorithms and analyzes the efficacy of implementing them on actually existing, rather than hypothetical, computing engines.

This book aims to cover the basics of this gamut of knowledge that a successful computational scientist needs to master. It is set up as a textbook for graduate students or advanced undergraduate students; others can use it as a reference text, reading the exercises for their information content.