Closed-Form Inverses of the Weakly Singular and Hypersingular Operators on Disks

R. Hiptmair; C. Jerez-Hanckes; C. Urzúa-Torres

doi:10.1007/s00020-018-2425-y

Closed-Form Inverses of the Weakly Singular and Hypersingular Operators on Disks

R. Hiptmair, C. Jerez-Hanckes, C. Urzúa-Torres

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We establish new explicit expressions and variational forms of boundary integral operators that provide the exact inverses of the weakly singular and hypersingular operators for - Δ on flat disks. We derive closed-form formulas for their singular kernels. We also show that the inverse of the weakly singular operator can be obtained by composing surface curl operators and the inverse of the hypersingular operator.

Original language	English
Article number	4
Journal	Integral Equations and Operator Theory
Volume	90
Issue number	1
DOIs	https://doi.org/10.1007/s00020-018-2425-y
State	Published - 1 Feb 2018
Externally published	Yes

Keywords

Boundary integral operators
Exact inverses
Projected spherical harmonics
Screens

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10.1007/s00020-018-2425-y

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abstract = "We establish new explicit expressions and variational forms of boundary integral operators that provide the exact inverses of the weakly singular and hypersingular operators for - Δ on flat disks. We derive closed-form formulas for their singular kernels. We also show that the inverse of the weakly singular operator can be obtained by composing surface curl operators and the inverse of the hypersingular operator.",

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N2 - We establish new explicit expressions and variational forms of boundary integral operators that provide the exact inverses of the weakly singular and hypersingular operators for - Δ on flat disks. We derive closed-form formulas for their singular kernels. We also show that the inverse of the weakly singular operator can be obtained by composing surface curl operators and the inverse of the hypersingular operator.

AB - We establish new explicit expressions and variational forms of boundary integral operators that provide the exact inverses of the weakly singular and hypersingular operators for - Δ on flat disks. We derive closed-form formulas for their singular kernels. We also show that the inverse of the weakly singular operator can be obtained by composing surface curl operators and the inverse of the hypersingular operator.

KW - Boundary integral operators

KW - Exact inverses

KW - Projected spherical harmonics

KW - Screens

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Closed-Form Inverses of the Weakly Singular and Hypersingular Operators on Disks

Abstract

Keywords

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