Guide to Numerical Algorithm Design and Development: Including Legacy Examples from Fortran and MathCAD in High Precision

by George Delic

Overview

The focus of this unique textbook/reference is on numerical algorithms that are stable and provide high precision in common numerical problems encountered in large-scale modeling projects.

The techniques presented are based on algorithms developed by the author over six decades of research and publications in peer-reviewed journals. The exposition includes topics typical of numerical analysis courses and is supplemented with examples of algorithms demonstrated in an engineering worksheet that is easy to read and comprehend. Each chapter ends with exercises and programming problems. Additional examples are available as downloadable Fortran code based on the author’s large-scale models in computational physics. The limitations of commodity processors and modern compilers is discussed, with advice provided on how to control them in an algorithm’s code design. An ample bibliography of over 200 citations provides a guide to further reading.

Topics, features, and emphases:

· Stability: knowing the range of algorithm parameters for producing reliable results

· Accuracy: understanding convergence to a result through quantitative metrics

· Precision: advance knowledge of the expected numerical precision and how to control it

· Efficiency: translating an algorithm into code with limited redundant computation

The primary target audience of this textbook/guide are senior graduate (or postgraduate) students in computer science and scientific or engineering fields who are starting on a career path as the next generation of model developers for high-performance computing (HPC). Additionally, the book will appeal to professionals engaged in large-scale computer model development who could use the volume as a course supplement or reference.

The author is an Honorary Fellow of the University of Wollongong, New South Wales, Australia. He is active as a private consultant in HPC and CEO of HiPERiSM Consulting, LLC, in the United States of America.

Product Details

ISBN-13:	9783031901775
Publisher:	Springer Nature Switzerland
Publication date:	07/31/2025
Series:	Texts in Computer Science
Pages:	484
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Dr. Delic majored in Physics for the B.S. (University of New South Wales) and received a Ph.D. in Theoretical Physics (Australian National University). He went on to establish a career in computational physics that spanned work at research and development centers in Europe and the USA. After this a tenured faculty appointment followed with academic duties in service, teaching and research. Dr. Delic's research record of over 50 peer-reviewed publications demonstrates a wide range of interests centered in advanced numerical algorithms for high performance computational platforms. He has more than three decades of programmer/analyst experience on serial, vector, Shared Memory Parallel and Distributed Memory Parallel computer platforms. After arrival in the USA Dr. Delic developed skills (and a training program) in vector Supercomputing and published research on Supercomputer work-load performance. He then entered into Government contracting where he acted as a Key Appointment in establishing the U.S. EPA Scientific Customer Support group at the EPA's Supercomputer Center. During this tenure Dr. Delic acted as project lead in software development, conducted outreach/training at customer sites, and organized/edited technical conferences/proceedings on Supercomputing and high performance algorithms for environmental models. Dr. Delic has applied his extensive experience in Government contracting to establish a consultancy (HiPERiSM Consulting, LLC) that specializes in technology transfer to enhance programmer skill levels in OpenMP, MPI and hybrid OpenMP+MPI programming. Specialized courses have sensitized stake-holders in legacy codes to the need for code and performance portability across current and future computer architectures. The importance of software tools and the programming environment as a whole have been major components of the consultancy. Dr. Delic's current interests include, evaluation of compiler performance, portability across parallel computer architectures, and hybrid programming models that match trends in clustered parallel computing.

Table of Contents

1.Number Systems and Machine Representation.- 2.Function Approximation and Error.- 3.Interpolation of Discrete Data.- 4.Function Approximation.- 5.Operator Equations and Notation.- 6.Finding Roots of Functions.- 7.One-dimensional Numerical Integration.- 8.Two-dimensional Numerical Integration.- 9.Numerical Solution of Ordinary Differential Equations.- 10.Direct Search Optimization Methods.