Bücher von Hans Petter Langtangen

This book is about solving partial differential equations (PDEs). Such equa- tions are used to model a wide range ofphenomena in virtually all fields ofsci- ence and technology. Inthe last decade, the general availability of extremely powerful computers has shifted the focus in computational mathematics from simplified model problems to much more sophisticated models resembling in- tricate features of real life. This change challenges our knowledge in computer science and in numerical analysis. The main objective ofthe present book is to teach modern,advanced tech- niques for numerical PDE solution. The book also introduces several models arising in fields likefinance, medicine, material technology, and geology. Inor- der to read this book, you must have a basic knowledge of partial differential equations and numerical methods for solving such equations. Furthermore, some background in finite element methods is required. You do not need to know Diffpack, although this programming environment is used in examples throughout the text. Basically, this book is about models, methods, and how to implement the methods. For the implementation part it is natural for us to use Diffpack as the programming environment, because making a PDE solver in Diffpack requires little amount of programming and because Diff- pack has support for the advanced numerical methods treated in this book. Most chapters have a part on models and methods, and a part on imple- mentation and Diffpack programming. The exposition is designed such that readers can focus only on the first part, if desired.

Looking back at the years that have passed since the realization of the very first electronic, multi-purpose computers, one observes a tremendous growth in hardware and software performance. Today, researchers and engi- neers have access to computing power and software that can solve numerical problems which are not fully understood in terms of existing mathemati- cal theory. Thus, computational sciences must in many respects be viewed as experimental disciplines. As a consequence, there is a demand for high- quality, flexible software that allows, and even encourages, experimentation with alternative numerical strategies and mathematical models. Extensibil- ity is then a key issue; the software must provide an efficient environment for incorporation of new methods and models that will be required in fu- ture problem scenarios. The development of such kind of flexible software is a challenging and expensive task. One way to achieve these goals is to in- vest much work in the design and implementation of generic software tools which can be used in a wide range of application fields. In order to provide a forum where researchers could present and discuss their contributions to the described development, an International Work- shop on Modern Software Tools for Scientific Computing was arranged in Oslo, Norway, September 16-18, 1996. This workshop, informally referred to as Sci Tools '96, was a collaboration between SINTEF Applied Mathe- matics and the Departments of Informatics and Mathematics at the Uni- versity of Oslo.

This textbook teaches finite element methods from a computational point of view. It focuses on how to develop flexible computer programs with Python, a programming language in which a combination of symbolic and numerical tools is used to achieve an explicit and practical derivation of finite element algorithms.

This book presents computer programming as a key method for solving mathematical problems. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students.

This book presents computer programming as a key method for solving mathematical problems. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style is more accessible and concise, in keeping with the needs of engineering students.

This text provides a very simple, initial introduction to the complete scientific computing pipeline: models, discretization, algorithms, programming, verification, and visualization.

The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biology, and most engineering disciplines. It is our goal to teach principles and ideas that carry over from field to field.

The goal of this book is to demonstrate how to develop tailored, flexible working environments built from small programs (scripts) written in the easy-to-learn, high-level language Python. The focus is on applications relevant to computational scientists.

The book serves both as a reference forvarious scaled models with corresponding dimensionless numbers, and as aresource for learning the art of scaling. The scientific literature is full of scaled models, but in mostof the cases, the scales are just stated without thorough mathematicalreasoning.