Solving for Micro- And Macro-Scale Electrostatic Configurations Using the Robin Hood Algorithm

Formaggio, J. A.; Lazić, Predrag; Corona, T.J.; Štefančić, Hrvoje; Abraham, Hrvoje; Gluck, and Ferenc

doi:10.2528/pierb11112106

Cited by 10 publications

(21 citation statements)

References 33 publications

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“…Although Wang et al used matrix pseudoinverse to compute the charge densities per-triangle, this has the drawback of requiring N 2 memory (where N is the number of triangles) to store and invert the matrix. An alternative technique called the Robin-Hood method, which has a space complexity proportional to N [Formaggio et al 2012], is used here instead. This technique randomly assigns charge densities to each triangle of the object surface, then redistributes the charge such that a consistent resulting potential is achieved across probe points on the object surface.…”

Section: Methodsmentioning

confidence: 99%

Model topology change with correspondence using electrostatics

Sandilands¹,

Komura²

2014

Proceedings of the 20th ACM Symposium on Virtual Reality Software and Technology

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This paper introduces a method for finding a dense correspondence between objects of varying topology or connectivity by using a proxy, genus zero mesh alongside the technique of Blended Intrinsic Maps. Harmonic space parameterisation is used to create a closed, genus zero shape that approximates the geometry of the original object. This allows for noisy or topologically different representations of objects to be mapped to one another, with seams in the mapping falling in generally hidden concave areas and tunnels. The paper presents example mapping between objects with and without holes, as well as objects that consist of a number of disconnected segments.

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Section: Methodsmentioning

confidence: 99%

Model topology change with correspondence using electrostatics

Sandilands¹,

Komura²

2014

Proceedings of the 20th ACM Symposium on Virtual Reality Software and Technology

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“…KEMField deals with large systems through the use of either the Robin Hood method, or Krylov subspace methods. The Robin Hood method, which is a special version of the Gauss-Seidel iteration, allows one to solve the linear system with a memory cost proportional to N ( ) and a computational cost which scales like N  a ( ) (with 1 2 a < < ) [27]. On the other hand, Krylov subspace methods such as GMRES [28], if used with straightforward matrix-vector multiplication, would by themselves generally be insufficient to efficiently solve problems of this size.…”

Section: Electric Fieldmentioning

confidence: 99%

Kassiopeia: a modern, extensible C++ particle tracking package

et al. 2017

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The KASSIOPEIA particle tracking framework is an object-oriented software package using modern C+ + techniques, written originally to meet the needs of the KATRIN collaboration. KASSIOPEIA features a new algorithmic paradigm for particle tracking simulations which targets experiments containing complex geometries and electromagnetic fields, with high priority put on calculation efficiency, customizability, extensibility, and ease-of-use for novice programmers. To solve KASSIOPEIAʼs target physics problem the software is capable of simulating particle trajectories governed by arbitrarily complex differential equations of motion, continuous physics processes that may in part be modeled as terms perturbing that equation of motion, stochastic processes that occur in flight such as bulk scattering and decay, and stochastic surface processes occurring at interfaces, including transmission and reflection effects. This entire set of computations takes place against the backdrop of a rich geometry package which serves a variety of roles, including initialization of electromagnetic field simulations and the support of state-dependent algorithm-swapping and behavioral changes as a particle's state evolves. Thanks to the very general approach taken by KASSIOPEIA it can be used by other experiments facing similar challenges when calculating particle trajectories in electromagnetic fields. It is publicly available at https://github.com/KATRIN-Experiment/Kassiopeia.

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“…Electric fields are computed by the boundary element method (BEM) from a set of charge densities at the electrode surfaces. The charge densities are pre-computed from the given electrode potentials with the iterative Robin Hood method [46]. For axially symmetric electric fields, an approximation method known as zonal harmonic expansion can be used to speed up the field computations with negligible loss of accuracy [47].…”

Section: Implementation Into Kassiopeiamentioning

confidence: 99%

A pulsed, mono-energetic and angular-selective UV photo-electron source for the commissioning of the KATRIN experiment

et al. 2017

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The KATRIN experiment aims to determine the neutrino mass scale with a sensitivity of 200 meV/c 2 (90% C. L.) by a precision measurement of the shape of the tritium β-spectrum in the endpoint region. The energy analysis of the decay electrons is achieved by a MAC-E filter spectrometer. To determine the transmission properties of the KATRIN main spectrometer, a mono-energetic and angularselective electron source has been developed. In preparation for the second commissioning phase of the main spectrometer, a measurement phase was carried out at the KATRIN monitor spectrometer where the device was operated in a MAC-E filter setup for testing. The results of these measurements are compared with simulations using the particletracking software "Kassiopeia", which was developed in the KATRIN collaboration over recent years.

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Solving for Micro- And Macro-Scale Electrostatic Configurations Using the Robin Hood Algorithm

Cited by 10 publications

References 33 publications

Model topology change with correspondence using electrostatics

Model topology change with correspondence using electrostatics

Kassiopeia: a modern, extensible C++ particle tracking package

A pulsed, mono-energetic and angular-selective UV photo-electron source for the commissioning of the KATRIN experiment

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