TY - JOUR
T1 - Harmonic density interpolation methods for high-order evaluation of Laplace layer potentials in 2D and 3D
AU - Pérez-Arancibia, Carlos
AU - Faria, Luiz M.
AU - Turc, Catalin
N1 - Funding Information:
Catalin Turc gratefully acknowledges support from NSF through contract DMS-1614270 . Luiz M. Faria gratefully acknowledges support from NSF through contract CMMI-1727565 .
Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2019/1/1
Y1 - 2019/1/1
N2 - We present an effective harmonic density interpolation method for the numerical evaluation of singular and nearly singular Laplace boundary integral operators and layer potentials in two and three spatial dimensions. The method relies on the use of Green's third identity and local Taylor-like interpolations of density functions in terms of harmonic polynomials. The proposed technique effectively regularizes the singularities present in boundary integral operators and layer potentials, and recasts the latter in terms of integrands that are bounded or even more regular, depending on the order of the density interpolation. The resulting boundary integrals can then be easily, accurately, and inexpensively evaluated by means of standard quadrature rules. A variety of numerical examples demonstrate the effectiveness of the technique when used in conjunction with the classical trapezoidal rule (to integrate over smooth curves) in two-dimensions, and with a Chebyshev-type quadrature rule (to integrate over surfaces given as unions of non-overlapping quadrilateral patches) in three-dimensions.
AB - We present an effective harmonic density interpolation method for the numerical evaluation of singular and nearly singular Laplace boundary integral operators and layer potentials in two and three spatial dimensions. The method relies on the use of Green's third identity and local Taylor-like interpolations of density functions in terms of harmonic polynomials. The proposed technique effectively regularizes the singularities present in boundary integral operators and layer potentials, and recasts the latter in terms of integrands that are bounded or even more regular, depending on the order of the density interpolation. The resulting boundary integrals can then be easily, accurately, and inexpensively evaluated by means of standard quadrature rules. A variety of numerical examples demonstrate the effectiveness of the technique when used in conjunction with the classical trapezoidal rule (to integrate over smooth curves) in two-dimensions, and with a Chebyshev-type quadrature rule (to integrate over surfaces given as unions of non-overlapping quadrilateral patches) in three-dimensions.
KW - Boundary integral operators
KW - Harmonic polynomials
KW - Laplace equation
KW - Layer potentials
KW - Nyström method
KW - Taylor interpolation
UR - http://www.scopus.com/inward/record.url?scp=85054423469&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2018.10.002
DO - 10.1016/j.jcp.2018.10.002
M3 - Article
SN - 0021-9991
VL - 376
SP - 411
EP - 434
JO - Journal of computational physics
JF - Journal of computational physics
ER -