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.

This publication includes 82 technical papers presented at Rocscience International Conference (RIC) 2021, held online on April 20 and 21, 2021. Rocscience created this event to bring geotechnical academics, researchers and practitioners together to exchange ideas as part of celebrating 25 years of the company’s existence. The papers in these proceedings were from keynotes, panel discussions and papers, selected after careful review of over 100 technical submissions delivered at RIC 2021. The technical papers were grouped into sessions based on their subject areas. The conference aimed to stimulate discussions that could help the industry work towards overcoming geotechnical engineering limitations today. It also sought to foster creative thinking that will advance the current states of the art and practice. The keynote addresses, panel discussions and technical presentations tried to examine geotechnical problems and situations from fresh perspectives. RIC 2021 hopes that the proceedings will continue to enrich our thinking and contribute to achieving a critical mass of change in our practices and approaches. We look forward to significant improvements in our industry.

A comprehensive, step-by-step reference to the Nyström Method for solving Electromagnetic problems using integral equations Computational electromagnetics studies the numerical methods or techniques that solve electromagnetic problems by computer programming. Currently, there are mainly three numerical methods for electromagnetic problems: the finite-difference time-domain (FDTD), finite element method (FEM), and integral equation methods (IEMs). In the IEMs, the method of moments (MoM) is the most widely used method, but much attention is being paid to the Nyström method as another IEM, because it possesses some unique merits which the MoM lacks. This book focuses on that method—providing information on everything that students and professionals working in the field need to know. Written by the top researchers in electromagnetics, this complete reference book is a consolidation of advances made in the use of the Nyström method for solving electromagnetic integral equations. It begins by introducing the fundamentals of the electromagnetic theory and computational electromagnetics, before proceeding to illustrate the advantages unique to the Nyström method through rigorous worked out examples and equations. Key topics include quadrature rules, singularity treatment techniques, applications to conducting and penetrable media, multiphysics electromagnetic problems, time-domain integral equations, inverse scattering problems and incorporation with multilevel fast multiple algorithm. Systematically introduces the fundamental principles, equations, and advantages of the Nyström method for solving electromagnetic problems Features the unique benefits of using the Nyström method through numerical comparisons with other numerical and analytical methods Covers a broad range of application examples that will point the way for future research The Nystrom Method in Electromagnetics is ideal for graduate students, senior undergraduates, and researchers studying engineering electromagnetics, computational methods, and applied mathematics. Practicing engineers and other industry professionals working in engineering electromagnetics and engineering mathematics will also find it to be incredibly helpful.

The papers in this volume were selected for presentation at the Fourth Annual International Computing and Combinatorics Conference (COCOON’98), held on August 12–14, 1998, in Taipei. The topics cover most aspects of theoretical computer science and combinatorics related to computing. Submissions to the conference this year was only conducted electronically. Thanks to the excellent software developed by the system team of the Institute of Information Science, we were able to make virtually all communications through the World Wide Web. A total of 69 papers was submitted in time to be considered, of which 36 papers were accepted for presentation at the conference. In addition to these contributed papers, the conference also included four invited presentations by Christo Papadimitriou, Michael Fishcher, Fan Chung Graham and Rao Kosaraju. It is expected that most of the accepted papers will appear in a more complete form in scienti?c journals. Moreover, selected papers will appear in a special issue of Theoretical Computer Science. We thank all program committee members, their support sta? and referees for excellent work within demanding time constraints. We thank all authors who submitted papers for consideration. We are especially grateful to our colleagues who worked hard and o?ered widely di?ering talents to make the conference both possible and enjoyable. August 1998 Wen-Lian Hsu and Ming-Yang Kao Program Co-chairs COCOON’98 Organization COCOON’98 is organized by the Institute of Information Science, Academia Sinica, Taipei, Taiwan, ROC and in cooperation with Institute of Information and Computing Machinery (IICM), Taiwan, ROC.

Most problems in science involve many scales in time and space. An example is turbulent ?ow where the important large scale quantities of lift and drag of a wing depend on the behavior of the small vortices in the boundarylayer. Another example is chemical reactions with concentrations of the species varying over seconds and hours while the time scale of the oscillations of the chemical bonds is of the order of femtoseconds. A third example from structural mechanics is the stress and strain in a solid beam which is well described by macroscopic equations but at the tip of a crack modeling details on a microscale are needed. A common dif?culty with the simulation of these problems and many others in physics, chemistry and biology is that an attempt to represent all scales will lead to an enormous computational problem with unacceptably long computation times and large memory requirements. On the other hand, if the discretization at a coarse level ignoresthe?nescale informationthenthesolutionwillnotbephysicallymeaningful. The in?uence of the ?ne scales must be incorporated into the model. This volume is the result of a Summer School on Multiscale Modeling and S- ulation in Science held at Boso ¤n, Lidingo ¤ outside Stockholm, Sweden, in June 2007. Sixty PhD students from applied mathematics, the sciences and engineering parti- pated in the summer school.

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