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\title{}{\bf Stochastic and randomized SVD based algorithms for solving boundary integral equations}
\author{}{Mozartova N.S. and Sabelfeld K.K.}
{\it Institute of Computational Mathematics and Mathematical Geophysics, \\ SBRAS, NSU, Novosibirsk}
{\it nmozartova@gmail.com, sabelfeld.karl@yahoo.de}
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In this talk we report on a stochastic boundary method
which can be considered as
a randomized version of the method of fundamental solutions (see \cite{1}).
We analyze the performance of the algorithm, and consider a practically interesting case,
the calculation of the capacitance for complicated molecules consisting of a family of overlapped spheres.
We focus on the problem of evaluation of derivatives on the boundary, and use a boundary integral equation
which involves both the solution and its derivatives. It implies, we deal with integral
equations of the first kind, which may be, generally, ill-conditioned. To construct the solution,
we use a randomized SVD based method for solving the discrete system of linear equations which in turn is
constructed by using a randomized Nystroem method. We give estimations of the error and the cost of the suggested
algorithm.
The work has been supported by RFBR under Grants 12-01-00635-a.
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\bibitem{1}
{\it K.K. Sabelfeld, N.S. Mozartova}.
Stochastic boundary collocation and spectral methods for solving PDEs.
Monte Carlo Methods and Applications, vol.18 (2012), issue 3, 217-263.
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