The Laplace equation in 3D domains with cracks: dual singularities with log terms and extraction of corresponding edge flux intensity functions

Samuel Shannon; Victor Peron; Zohar Yosibash

doi:10.1002/mma.3562

The Laplace equation in 3D domains with cracks: dual singularities with log terms and extraction of corresponding edge flux intensity functions

Samuel Shannon, Victor Peron, Zohar Yosibash^*

^*Corresponding author for this work

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

1 Scopus citations

Abstract

The singular solution of the Laplace equation with a straight crack is represented by a series of eigenpairs, shadows, and their associated edge flux intensity functions (EFIFs). We address the computation of the EFIFs associated with the integer eigenvalues by the quasi-dual function method (QDFM). The QDFM is based on the dual eigenpairs and shadows, and we exhibit the presence of logarithmic terms in the dual singularities associated with the integer eigenvalues. These are then used with the QDFM to extract EFIFs from p-version finite element solutions. Numerical examples are provided.

Original language	English
Pages (from-to)	4951-4963
Number of pages	13
Journal	Mathematical Methods in the Applied Sciences
Volume	39
Issue number	17
DOIs	https://doi.org/10.1002/mma.3562
State	Published - 30 Nov 2016
Externally published	Yes

Keywords

3D singularities
dual eigenvalues
dual singularities
edge flux/stress intensity functions
logarithmic singularities
quasi-dual function method

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10.1002/mma.3562

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abstract = "The singular solution of the Laplace equation with a straight crack is represented by a series of eigenpairs, shadows, and their associated edge flux intensity functions (EFIFs). We address the computation of the EFIFs associated with the integer eigenvalues by the quasi-dual function method (QDFM). The QDFM is based on the dual eigenpairs and shadows, and we exhibit the presence of logarithmic terms in the dual singularities associated with the integer eigenvalues. These are then used with the QDFM to extract EFIFs from p-version finite element solutions. Numerical examples are provided.",

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T2 - dual singularities with log terms and extraction of corresponding edge flux intensity functions

AU - Shannon, Samuel

AU - Peron, Victor

AU - Yosibash, Zohar

PY - 2016/11/30

Y1 - 2016/11/30

N2 - The singular solution of the Laplace equation with a straight crack is represented by a series of eigenpairs, shadows, and their associated edge flux intensity functions (EFIFs). We address the computation of the EFIFs associated with the integer eigenvalues by the quasi-dual function method (QDFM). The QDFM is based on the dual eigenpairs and shadows, and we exhibit the presence of logarithmic terms in the dual singularities associated with the integer eigenvalues. These are then used with the QDFM to extract EFIFs from p-version finite element solutions. Numerical examples are provided.

AB - The singular solution of the Laplace equation with a straight crack is represented by a series of eigenpairs, shadows, and their associated edge flux intensity functions (EFIFs). We address the computation of the EFIFs associated with the integer eigenvalues by the quasi-dual function method (QDFM). The QDFM is based on the dual eigenpairs and shadows, and we exhibit the presence of logarithmic terms in the dual singularities associated with the integer eigenvalues. These are then used with the QDFM to extract EFIFs from p-version finite element solutions. Numerical examples are provided.

KW - 3D singularities

KW - dual eigenvalues

KW - dual singularities

KW - edge flux/stress intensity functions

KW - logarithmic singularities

KW - quasi-dual function method

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JO - Mathematical Methods in the Applied Sciences

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ER -

The Laplace equation in 3D domains with cracks: dual singularities with log terms and extraction of corresponding edge flux intensity functions

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