The Rapid Evaluation Of Potential Fields In Particle Systems

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 book and its companion volume, LNCS vols. 7331 and 7332, constitute the Proceedings of the Third International conference on Swarm Intelligence, ICSI 2012, held in Shenzhen, China in June 2012. The 145 full papers presented were carefully reviewed and selected from 247 submissions. The papers are organized in 27 cohesive sections covering all major topics of swarm intelligence research and developments.

This volume contains the proceedings of the 1998 International Conference on Simulation of Semiconductor Processes and Devices and provides an open forum for the presentation of the latest results and trends in modeling and simulation of semiconductor equipment, processes and devices. Topics include: • semiconductor equipment simulation • process modeling and simulation • device modeling and simulation of complex structures • interconnect modeling • integrated systems for process, device, circuit simulation and optimisation • numerical methods and algorithms • compact modeling and parameter extraction • modeling for RF applications • simulation and modeling of new devices (heterojunction based, SET’s, quantum effect devices, laser based ...)

This book constitutes the refereed proceedings of the 28th International Supercomputing Conference, ISC 2013, held in Leipzig, Germany, in June 2013. The 35 revised full papers presented together were carefully reviewed and selected from 89 submissions. The papers cover the following topics: scalable applications with 50K+ cores; performance improvements in algorithms; accelerators; performance analysis and optimization; library development; administration and management of supercomputers; energy efficiency; parallel I/O; grid and cloud.

Special functions enable us to formulate a scientific problem by reduction such that a new, more concrete problem can be attacked within a well-structured framework, usually in the context of differential equations. A good understanding of special functions provides the capacity to recognize the causality between the abstractness of the mathematical concept and both the impact on and cross-sectional importance to the scientific reality. The special functions to be discussed in this monograph vary greatly, depending on the measurement parameters examined (gravitation, electric and magnetic fields, deformation, climate observables, fluid flow, etc.) and on the respective field characteristic (potential field, diffusion field, wave field). The differential equation under consideration determines the type of special functions that are needed in the desired reduction process. Each chapter closes with exercises that reflect significant topics, mostly in computational applications. As a result, readers are not only directly confronted with the specific contents of each chapter, but also with additional knowledge on mathematical fields of research, where special functions are essential to application. All in all, the book is an equally valuable resource for education in geomathematics and the study of applied and harmonic analysis. Students who wish to continue with further studies should consult the literature given as supplements for each topic covered in the exercises.

Design Automation Methods and Tools for Microfluidics-Based Biochips deals with all aspects of design automation for microfluidics-based biochips. Experts have contributed chapters on many aspects of biochip design automation. Topics covered include: device modeling; adaptation of bioassays for on-chip implementations; numerical methods and simulation tools; architectural synthesis, scheduling and binding of assay operations; physical design and module placement; fault modeling and testing; and reconfiguration methods.

Boundary element methods relate to a wide range of engineering applications, including fluid flow, fracture analysis, geomechanics, elasticity, and heat transfer. Thus, new results in the field hold great importance not only to researchers in mathematics, but to applied mathematicians, physicists, and engineers. A two-day minisymposium Mathematical Aspects of Boundary Element Methods at the IABEM conference in May 1998 brought together top rate researchers from around the world, including Vladimir Maz’ya, to whom the conference was dedicated. Focusing on the mathematical and numerical analysis of boundary integral operators, this volume presents 25 papers contributed to the symposium. Mathematical Aspects of Boundary Element Methods provides up-to-date research results from the point of view of both mathematics and engineering. The authors detail new results, such as on nonsmooth boundaries, and new methods, including domain decomposition and parallelization, preconditioned iterative techniques, multipole expansions, higher order boundary elements, and approximate approximations. Together they illustrate the connections between the modeling of applied problems, the derivation and analysis of corresponding boundary integral equations, and their efficient numerical solutions.