Joe Pitt-Francis - Guide to Scientific Computing in C++

Advisory Board

Samson Abramsky, University of Oxford, Oxford, UK

Chris Hankin, Imperial College London, London, UK

Mike Hinchey, University of Limerick, Limerick, Ireland

Dexter C. Kozen, Cornell University, Ithaca, USA

Andrew Pitts, University of Cambridge, Cambridge, UK

Hanne Riis Nielson, Technical University of Denmark, Kongens Lyngby, Denmark

Steven S. Skiena, Stony Brook University, Stony Brook, USA

Iain Stewart, University of Durham, Durham, UK

Undergraduate Topics in Computer Science (UTiCS) delivers high-quality instructional content for undergraduates studying in all areas of computing and information science. From core foundational and theoretical material to final-year topics and applications, UTiCS books take a fresh, concise, and modern approach and are ideal for self-study or for a one- or two-semester course. The texts are all authored by established experts in their fields, reviewed by an international advisory board, and contain numerous examples and problems. Many include fully worked solutions.

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The principle changes in this updated edition are additional material on software testing and on some of the new features introduced in the C++11 standard. When introducing this additional material, we have followed the same philosophy as when writing the first edition of this book. That is, we focus on a concise discussion of the key features that are most useful to the novice and intermediate programmer in the field of scientific computing. We have found this an effective approach when teaching this course to graduate studentsonce the basics have been mastered, students then have the confidence to find out about less well-used features themselves when they are needed.

This second edition would not be as completeor as enjoyable to updatewithout discussions with colleagues and other readers of the first edition, including those previously unknown to us who were kind enough to provide constructive feedback. We would like to express our gratitude to all who contributed in this way or offered their encouragement, and to the staff at Springer for inviting us to update the first edition.

Finally, we would both again like to thank our families for their love and support.

Many books have been written on the C++ programming language, varying across a spectrum from the very practical to the very theoretical. This book certainly lies at the practical end of this spectrum and has a particular focus for the practical treatment of this language: scientific computing.

Traditionally, Fortran and MATLAB have been the languages of choice for scientific computing applications. The recent development of complex mathematical modelsin fields as diverse as biology, finance and materials science, to name but a fewhas driven a need for software packages that allow computational simulations based on these models. The complexity of the underlying models, together with the need to exchange code between co-workers, has motivated programmers to develop object-oriented code (often written in C++) for these simulation packages. The computational demands of these simulations may require software to be written for parallel computing facilities, typically using the Message Passing Interface (MPI). The need to train programmers in the skills to program applications such as these led to the development of a graduate-level course C++ for Scientific Computing , taught by the authors of this book, at the University of Oxford.

This book provides a guide to C++ programming in scientific computing. In contrast to many other books on C++, features of the language are demonstrated mainly using examples drawn from scientific computing. Object orientation is first mentioned in Chap. 1 where we briefly describe what this phraseand other related terms such as inheritancemeans, before postponing any further discussion of object orientation or related topics until Chap. 6. In the intervening chapters until object orientation reappears, we present what is best described as procedural programming in C++, covering variables, flow of control, input and output, pointers (including dynamic allocation of memory), functions and reference variables. Armed with this grounding in C++, we then introduce classes in Chaps. 6 and 7. In these two chapters, where the main features of object orientation are showcased, we initially, for the sake of clarity, abandon our principle of using examples drawn from scientific computing. Once the topics have been presented however, we resume our strategy of demonstrating concepts through scientific computing examples. More advanced C++ features such as templates and exceptions are introduced in Chaps. 8 and 9. Having introduced the features of C++ required for scientific computing, the remainder of the book focuses on the application of these features. In Chap. 10, we begin to develop a collection of classes for linear algebra calculations: these classes are then developed further in the exercises at the end of this chapter. Chapter 11 presents an introduction to parallel computing using MPI. Finally, in Chap. 12, we discuss how an object-oriented library for solving second-order differential equations may be constructed. The importance of a clear programming style to minimise the introduction of errors into code is stressed throughout the book.