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\title{}{\bf A spectral inversion of the spherical Poisson integral equation for solving PDEs: performance analysis}
\author{}{Sabelfeld K.K. and Levykin A.I. }
{\it Institute of Computational Mathematics and Mathematical Geophysics, \\ SBRAS, NSU, Novosibirsk}
{\it sabelfeld.karl@yahoo.de, lai@osmf.sscc.ru}
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Many practically interesting problems can be well described by PDEs for domains consisting of
a set of overlapped discs, planes (2D), balls and half-spaces (3D) (e.g., see the references in \cite{1}).
Conventional approach based on a refinement grid near the singular points may lead to accuracy decreasing and
computer memory problems, especially for large-scale 3D problems. We report on the performance of the
spectral method suggested in \cite{1} which is based on the inversion of the plane and spherical Poisson type
integral relations. We present the results of numerical simulations and give estimations of the accuracy
as functions of the number of harmonics used, the cut-off around the singularities, and estimate the cost
as well.
The work has been supported by RFBR under Grant 12-01-00635-a.
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\bibitem{1}
{\it Sabelfeld K.K.}
A stochastic spectral projection method for solving PDEs in domains composed by overlapping
discs, spheres, and half-spaces. Applied Mathematics and Computation,
Volume 219 (2013), Issue 10, Pages 5123–5139.
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