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- W3100668532 abstract "Abstract We propose fast cubature formulas for the elastic and hydrodynamic potentials based on the approximate approximation of the densities with Gaussian and related functions. For densities with separated representation, we derive a tensor product representation of the integral operator which admits efficient cubature procedures. We obtain high order approximations up to a small saturation error, which is negligible in computations. Results of numerical experiments which show approximation order $$mathscr {O}(h^{2M})$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mi>h</mml:mi> <mml:mrow> <mml:mn>2</mml:mn> <mml:mi>M</mml:mi> </mml:mrow> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , $$M=1,2,3,4$$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mrow> <mml:mi>M</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2</mml:mn> <mml:mo>,</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> , are provided." @default.
- W3100668532 created "2020-11-23" @default.
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- W3100668532 date "2020-11-10" @default.
- W3100668532 modified "2023-10-16" @default.
- W3100668532 title "Fast computation of elastic and hydrodynamic potentials using approximate approximations" @default.
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- W3100668532 doi "https://doi.org/10.1007/s13324-020-00400-4" @default.
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