We study high order cubature formulas for the computation of harmonic potentials over the n-dimensional half-space within the framework of approximate approximations. The cubature of the potentials is reduced to the quadrature of one-dimensional integrals over the half-line. In addition to a formula for general densities with bounded support on the half-space, we derive a tensor product representation of the integral operator which admits efficient cubature procedures for densities with separated approximation in very high space dimensions. Numerical experiments for the half-space up to dimension n = 106 confirm the predicted approximation errors. Bibliography: 11 titles. © 2011 Springer Science+Business Media, Inc.

Accurate cubature of volume potentials over high-dimensional half-spaces / Lanzara, Flavia; V. G., Maz'Ya; G., Schmidt. - In: JOURNAL OF MATHEMATICAL SCIENCES. - ISSN 1072-3374. - STAMPA. - 173:6(2011), pp. 683-700. [10.1007/s10958-011-0267-0]

Accurate cubature of volume potentials over high-dimensional half-spaces

LANZARA, Flavia;
2011

Abstract

We study high order cubature formulas for the computation of harmonic potentials over the n-dimensional half-space within the framework of approximate approximations. The cubature of the potentials is reduced to the quadrature of one-dimensional integrals over the half-line. In addition to a formula for general densities with bounded support on the half-space, we derive a tensor product representation of the integral operator which admits efficient cubature procedures for densities with separated approximation in very high space dimensions. Numerical experiments for the half-space up to dimension n = 106 confirm the predicted approximation errors. Bibliography: 11 titles. © 2011 Springer Science+Business Media, Inc.
2011
01 Pubblicazione su rivista::01a Articolo in rivista
Accurate cubature of volume potentials over high-dimensional half-spaces / Lanzara, Flavia; V. G., Maz'Ya; G., Schmidt. - In: JOURNAL OF MATHEMATICAL SCIENCES. - ISSN 1072-3374. - STAMPA. - 173:6(2011), pp. 683-700. [10.1007/s10958-011-0267-0]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/44206
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