Transonic accretion onto astrophysical objects is a unique example of analogue black hole realized in nature. In the framework of acoustic geometry we study axially symmetric accretion and wind of a rotating astrophysical black hole or of a neutron star assuming isentropic flow of a fluid described by a polytropic equation of state. In particular we analyze the causal structure of multitransonic configurations with two sonic points and a shock. Retarded and advanced null curves clearly demonstrate the presence of the acoustic black hole at regular sonic points and of the white hole at the shock. We calculate the analogue surface gravity and the Hawking temperature for the inner and outer acoustic horizons.

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.

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 nonlocal 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 α , where α < 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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We demonstrate practically approximation-free electrostatic calculations of micromesh detectors that can be extended to any other type of micropattern detectors. Using newly developed Boundary Element Method called Robin Hood Method we can easily handle objects with huge number of boundary elements (hundreds of thousands) without any compromise in numerical accuracy. In this paper we show how such calculations can be applied to Micromegas detectors by comparing electron transparencies and gains for four different types of meshes. We demonstrate inclusion of dielectric material by calculating the electric field around different types of dielectric spacers.

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