Open Access

ARTICLE

Hyper-Singular Dual Reciprocity Formulation for Potential Problems

C. F. Loeffler¹, R. G. Peixoto²

1 DEM/PPGEM, Federal University of Espírito Santo, Brazil.
2 SAMARCO MINERAÇÃO, Brazil.

Computer Modeling in Engineering & Sciences 2013, 93(4), 253-276. https://doi.org/10.3970/cmes.2013.093.253

Abstract

Here is presented a formal deduction for the Dual Reciprocity hypersingular boundary integral equation for application to two dimensional potential problems. The theoretical and numerical derivations are presented in detail, and some simple test problems are included to verify the accuracy of the proposed formulation. Due to its simplicity, Poisson’s Equation is used as a basis for the mathematical formulations and operational procedures related to the body force term, but the methodology can easily be extended to other more elaborate classes of potential problems. Poles are inserted internally to improve the interpolation within the domain, resulting in a hybrid singular and hyper-singular matrix system and global polynomial functions are also implemented for the same purpose. Problems belonging to scalar field theory that have known analytical solutions are solved, in order to obtain a preliminarily assessment of the efficiency and capability of the technique for more elaborate applications.

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Keywords

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