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| Home > Publications database > Fast Methods for Long-Range Interactions in Complex Systems |
| Book | PreJuSER-16155 |
; ;
2011
Forschungszentrum Jülich Gmbh Zentralbibliothek, Verlag
Jülich
ISBN: 978-3-89336-714-6
Please use a persistent id in citations: http://hdl.handle.net/2128/4441
Abstract: Computer simulations of complex particle systems have a still increasing impact in a broad field of physics, e.g. astrophysics, statistical physics, plasma physics, material sciences, physical chemistry or biophysics, to name a few. Along with the development of computer hardware, which today shows a performance in the range of PFlop/s, it is essential to develop efficient and scalable algorithms which solve the physical problem. Since with more powerful computer systems usually also the problem size is increased, it is important to implement optimally scaling algorithms, which increase the computational effort proportionally to the number of particles. Especially in fields, where long-range interactions between particles have to be considered the numerical effort is usually very large. Since most of interesting physical phenomena involve electrostatic, gravitational or hydrodynamic effects, the proper inclusion of long range interactions is essential for the correct description of systems of interest. Since in principle, long range interactions are O(N$^{2}$) for open systems or include infinite lattice sums in periodic systems, fast implementations rely on approximations. Although, in principle, various methods might be considered as $\textit{exact representations}$ of the problem, approximations with controllable error thresholds are developed. Since different boundary conditions or dielectric properties require the application of appropriate methods, there is not only one method, but various classes of methods developed. E.g. the inclusion of different symmetries in the system (1d- ,2d- or 3d-periodic systems), the presence of interfaces or including inhomogeneous dielectric properties, require the implementation of different electrostatic methods. Furthermore, the interdisciplinary character of the problem led to the fact that either very similar methods or complementary methods were developed independently in parallel in different disciplines or were $\textit{discovered}$ in other research areas and adopted to other fields. Therefore the present school does not only focus on one method, but intrduces a spectrum of different fast algorithms: [...]
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