dorsal/arxiv
View SchemaThe Robin Hood method - a novel numerical method for electrostatic problems based on a non-local charge transfer
| Authors | Predrag Lazic, Hrvoje Stefancic, Hrvoje Abraham |
|---|---|
| Categories | |
| ArXiv ID | physics/0411192 |
| URL | https://arxiv.org/abs/physics/0411192 |
Abstract
We introduce a novel numerical method, named the Robin Hood method, of solving electrostatic problems. The approach of the method is closest to the boundary element methods, although significant conceptual differences exist with respect to this class of methods. The method achieves equipotentiality of conducting surfaces by iterative non-local charge transfer. For each of the conducting surfaces non-local charge transfers are performed between surface elements which differ the most from the targeted equipotentiality of the surface. The method is tested against analytical solutions and its wide range of application is demonstrated. The method has appealing technical characteristics. For the problem with N surface elements, the computational complexity of the method essentially scales with N^alpha, where alpha < 2, the required computer memory scales with N, while the error of the potential decreases exponentially with the number of iterations for many orders of magnitude of the error, without the presence of the Critical Slowing Down. The Robin Hood method has a large potential of application in other classical as well as quantum problems. Some possible applications outside electrostatics are outlined.
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"abstract": "We introduce a novel numerical method, named the Robin Hood method, of\nsolving electrostatic problems. The approach of the method is closest to the\nboundary element methods, although significant conceptual differences exist\nwith respect to this class of methods. The method achieves equipotentiality of\nconducting surfaces by iterative non-local charge transfer. For each of the\nconducting surfaces non-local charge transfers are performed between surface\nelements which differ the most from the targeted equipotentiality of the\nsurface. The method is tested against analytical solutions and its wide range\nof application is demonstrated. The method has appealing technical\ncharacteristics. For the problem with N surface elements, the computational\ncomplexity of the method essentially scales with N^alpha, where alpha \u003c 2, the\nrequired computer memory scales with N, while the error of the potential\ndecreases exponentially with the number of iterations for many orders of\nmagnitude of the error, without the presence of the Critical Slowing Down. The\nRobin Hood method has a large potential of application in other classical as\nwell as quantum problems. Some possible applications outside electrostatics are\noutlined.",
"arxiv_id": "physics/0411192",
"authors": [
"Predrag Lazic",
"Hrvoje Stefancic",
"Hrvoje Abraham"
],
"categories": [
"physics.comp-ph",
"physics.class-ph"
],
"title": "The Robin Hood method - a novel numerical method for electrostatic problems based on a non-local charge transfer",
"url": "https://arxiv.org/abs/physics/0411192"
},
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