The evaluation of Coulombic or gravitational interactions in large ensembles of particles is an integral part of the numerical simulation of a large number of physical processes. Examples include celestial mechanics, plasma physics, the vortex method in fluid dynamics, molecular dynamics, molecular dynamics, and the solution of the Laplace equation via potential theory. A numerical model follows the trajectories of a number of particles moving in accordance with Newton's second law of motion in a field generated by the whole ensemble. In many situations, in order to be of physical interest, the simulation has to involve thousands of particles (or more), and the fields have to be evaluated for a large number of configurations. Unfortunately, an amount of work of the order O N-sg has traditionally been required to evaluate all pairwise interactions in a system of N particles, unless some approximation or truncation method is used. Large scale simulations have been extremely expensive in some cases, and prohibitive in others. An algorithm is presented for the rapid evaluation of the potential and force fields in large scale systems of particles. To evaluate all pairwise Coulombic interactions of N particles to within round off error, the algorithm requires an amount of work proportional to N, and this estimate does not depend on the statistics of the distribution. Both two and three dimensional versions of the algorithm have been constructed. Applications to several problems in physics, chemistry, biology, and numerical complex analysis are discussed.

Molecular simulation allows researchers unique insight into the structures and interactions at play in fluids. Since publication of the first edition of Molecular Simulation of Fluids, novel developments in theory, algorithms and computer hardware have generated enormous growth in simulation capabilities. This 2nd edition has been fully updated and expanded to highlight this recent progress, encompassing both Monte Carlo and molecular dynamic techniques, and providing details of theory, algorithms and both serial and parallel implementations. Beginning with a clear introduction and review of theoretical foundations, the book goes on to explore intermolecular potentials before discussing the calculation of molecular interactions in more detail. Monte Carlo simulation and integrators for molecular dynamics are then discussed further, followed by non-equilibrium molecular dynamics and molecular simulation of ensembles and phase equilibria. The use of object-orientation is examined in detail, with working examples coded in C++. Finally, practical parallel simulation algorithms are discussed using both MPI and GPUs, with the latter coded in CUDA. Drawing on the extensive experience of its expert author, Molecular Simulation of Fluids: Theory, Algorithms, Object-Orientation, and Parallel Computing 2nd Edition is a practical, accessible guide to this complex topic for all those currently using, or interested in using, molecular simulation to study fluids. Fully updated and revised to reflect advances in the field, including new chapters on intermolecular potentials and parallel algorithms Covers the application of both MPI and GPU programming to molecular simulation Covers a wide range of simulation topics using both Monte Carlo and molecular dynamics approaches Provides access to downloadable simulation code, including GPU code using CUDA, to encourage practice and support learning

Employed in a large number of commercial electromagnetic simulation packages, the finite element method is one of the most popular and well-established numerical techniques in engineering. This book covers the theory, development, implementation, and application of the finite element method and its hybrid versions to electromagnetics. FINITE ELEMENT METHOD FOR ELECTROMAGNETICS begins with a step-by-step textbook presentation of the finite method and its variations then goes on to provide up-to-date coverage of three dimensional formulations and modern applications to open and closed domain problems. Worked out examples are included to aid the reader with the fine features of the method and the implementation of its hybridization with other techniques for a robust simulation of large scale radiation and scattering. The crucial treatment of local boundary conditions is carefully worked out in several stages in the book. Sponsored by: IEEE Antennas and Propagation Society.

This book details the necessary numerical methods, the theoretical background and foundations and the techniques involved in creating computer particle models, including linked-cell method, SPME-method, tree codes, amd multipol technique. It illustrates modeling, discretization, algorithms and their parallel implementation with MPI on computer systems with distributed memory. The text offers step-by-step explanations of numerical simulation, providing illustrative code examples. With the description of the algorithms and the presentation of the results of various simulations from fields such as material science, nanotechnology, biochemistry and astrophysics, the reader of this book will learn how to write programs capable of running successful experiments for molecular dynamics.

Big Data of Complex Networks presents and explains the methods from the study of big data that can be used in analysing massive structural data sets, including both very large networks and sets of graphs. As well as applying statistical analysis techniques like sampling and bootstrapping in an interdisciplinary manner to produce novel techniques for analyzing massive amounts of data, this book also explores the possibilities offered by the special aspects such as computer memory in investigating large sets of complex networks. Intended for computer scientists, statisticians and mathematicians interested in the big data and networks, Big Data of Complex Networks is also a valuable tool for researchers in the fields of visualization, data analysis, computer vision and bioinformatics. Key features: Provides a complete discussion of both the hardware and software used to organize big data Describes a wide range of useful applications for managing big data and resultant data sets Maintains a firm focus on massive data and large networks Unveils innovative techniques to help readers handle big data Matthias Dehmer received his PhD in computer science from the Darmstadt University of Technology, Germany. Currently, he is Professor at UMIT – The Health and Life Sciences University, Austria, and the Universität der Bundeswehr München. His research interests are in graph theory, data science, complex networks, complexity, statistics and information theory. Frank Emmert-Streib received his PhD in theoretical physics from the University of Bremen, and is currently Associate professor at Tampere University of Technology, Finland. His research interests are in the field of computational biology, machine learning and network medicine. Stefan Pickl holds a PhD in mathematics from the Darmstadt University of Technology, and is currently a Professor at Bundeswehr Universität München. His research interests are in operations research, systems biology, graph theory and discrete optimization. Andreas Holzinger received his PhD in cognitive science from Graz University and his habilitation (second PhD) in computer science from Graz University of Technology. He is head of the Holzinger Group HCI-KDD at the Medical University Graz and Visiting Professor for Machine Learning in Health Informatics Vienna University of Technology.