The Robin Hood method—A new view on differential equations

Lazić, Predrag; Štefančić, Hrvoje; Abraham, Hrvoje

doi:10.1016/j.enganabound.2007.06.004

Cited by 7 publications

(14 citation statements)

References 9 publications

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“…The largest cube calculated was represented by 202,800 triangles, obtaining a capacitance value of 0.66067786±8×10 −8 in units of 1/4π 0 . The calculation represents one of the most accurate values of the capacitance of the cube calculated to date [7,8]. The algorithm is not limited in terms of the number of triangles employed and, when used in combination with parallel processing, can be remarkably fast and efficient.…”

Section: Verification Examplesmentioning

confidence: 99%

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

Formaggio¹,

Lazić²,

Corona³

et al. 2012

PIER B

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Abstract-We present a novel technique by which highly-segmented electrostatic configurations can be solved. The Robin Hood method is a matrix-inversion algorithm optimized for solving high density boundary element method (BEM) problems.We illustrate the capabilities of this solver by studying two distinct geometry scales: (a) the electrostatic potential of a large volume beta-detector and (b) the field enhancement present at surface of electrode nano-structures. Geometries with elements numbering in the O(10 5 ) are easily modeled and solved without loss of accuracy. The technique has recently been expanded so as to include dielectrics and magnetic materials.

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Section: Verification Examplesmentioning

confidence: 99%

“…The technique was first introduced in 2006 [7,8], and was recently expanded to include dielectric and magnetic materials. We illustrate its applicability and scope by studying both micro-and macro-scale systems.…”

Section: Introductionmentioning

confidence: 99%

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

Formaggio¹,

Lazić²,

Corona³

et al. 2012

PIER B

Self Cite

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“…We also compared the value of potential with estimates for the barycenter and other field point values as obtained from [14,15], the expression having been slightly modified. At the barycenter, the expression given is exact, whereas, the multipole (monopole+quadrupole) expression is expected to be valid at any arbitrary location.…”

Section: Comparison With Multipole Expressionsmentioning

confidence: 99%

“…Despite a large body of literature, closed form analytic expressions for computing the effects of distributed singularities are rare [11,12], complicated to implement and, often, valid only for special cases [13,14,15]. For example, in [11], the integration of the Green function to compute the influence of a constant source distribution is modified to an "nplane" integration.…”

Section: Introductionmentioning

confidence: 99%

A study of three-dimensional edge and corner problems using the neBEM solver

Mukhopadhyay

Majumdar

2009

Engineering Analysis with Boundary Elements

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The previously reported neBEM solver has been used to solve electrostatic problems having three-dimensional edges and corners in the physical domain. Both rectangular and triangular elements have been used to discretize the geometries under study. In order to maintain very high level of precision, a library of C functions yielding exact values of potential and flux influences due to uniform surface distribution of singularities on flat triangular and rectangular elements has been developed and used. Here we present the exact expressions proposed for computing the influence of uniform singularity distributions on triangular elements and illustrate their accuracy. We then consider several problems of electrostatics containing edges and singularities of various orders including plates and cubes, and L-shaped conductors. We have tried to show that using the approach proposed in the earlier paper on neBEM and its present enhanced (through the inclusion of triangular elements) form, it is possible to obtain accurate estimates of integral features such as the capacitance of a given conductor and detailed ones such as the charge density distribution at the edges / corners without taking resort to any new or special formulation. Results obtained using neBEM have been compared extensively with both existing analytical and numerical results. The comparisons illustrate the accuracy, flexibility and robustness of the new approach quite comprehensively.

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“…The surfaces are assumed to be conducting so that (after long enough time) the electric potential is constant on the surface and the electric field vector is everywhere perpendicular to the surface. Surfaces are represented by triangles and the electrostatic problem is solved using the boundary element formulation as implemented in the state-of-the-art Robin Hood code [8]. Only in the boundary element approach one can obtain accurate electric field values, especially around spikes.…”

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confidence: 99%

Surface-roughness–induced electric-field enhancement and triboluminescence

Lazić¹,

Persson²

2010

EPL

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The separation of solids in adhesive contact, or the fracture of solid bodies, often results in the emission of high energy photons, e.g., visible light and X-rays. This is believed to be related to charge separation. We propose that the emission of high energy photons involves surface roughness and surface diffusion of ions or electrons, resulting in the concentration of charge at the tips of high asperities, and to electric field enhancement, which facilitate the discharging process which result in the high energy photons. If the surface diffusion is too fast, or the separation of the solid surfaces too slow, discharging start at small interfacial separation resulting in low energy photons.The relative motion between two contacting solids can produce light, called triboluminescence [1,2]. For example, opening an envelope in a dark room usually result in flashes of blue light from the (pressure sensitive rubber) adhesive interface. Recent experiment have shown that photons with energies up to ∼ 100 keV are produced during the pealing of adhesive tape in 10 −3 Torr vacuum. The X-ray pulses were of nano-second duration, produced ∼ 100 mW, and were correlated with stick-slip peeling events.The origin of triboluminescence is believed to be related to charge separation. In order for charge separation to generate high energy photons, the discharging process must not occur until the solid walls have been separated by a relative large distance. If the surface charge density is denoted by ±σ = ±n 0 e (where e is the electron charge and n 0 the ion number density), and if the charge is uniformly distributed, the voltage drop between the two separating surfaces is given by V = Ed = 4πσd where d is the surface separation. The highest energy photons (energyhω max ) emitted during the discharging is likely to behω max = eV = 4πn 0 e 2 d, and will have an energy proportional to the surface separation at the moment of the discharge. In a typical experiment the average surface charge density n 0 ≈ 10 14 m −2 so that if the discharging would occur at the separation d ≈ 1 mm one would expect photons with energy up to a few keV. In the experiment reported on in Ref.[3] photons with energies up to 100 keV were observed, indicating even higher local charge concentration.In vacuum the initiation of the discharging must be related to field assisted emission. That is, such a strong electric field must be set up at the surface of at least one of the solids that electrons or ions are pulled away from the surface. This may involve tunneling (mainly for electrons) or thermally induced charge transfer (or a combination of both) across or over the barrier towards desorption. The charged particle is then accelerated by the electric field, and when it hits into the surface of the opposite solid it may generate photons (bremsstrahlung) and produce more charged particles, some of which (of opposite sign as the impacting particle) may accelerate towards the opposite solid and in this way generate a cascade of charged particles and photons. This m...

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The Robin Hood method—A new view on differential equations

Cited by 7 publications

References 9 publications

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

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

A study of three-dimensional edge and corner problems using the neBEM solver

Surface-roughness–induced electric-field enhancement and triboluminescence

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