.png){kind=icon}
.png){kind=icon}
Return
Corrected trapezoidal rules for singular implicit boundary integrals
.png){kind=icon}
OA
AI
DOI：10.1016/j.jcp.2022.111193.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
We present new higher-order quadratures for a family of boundary integral operators re derived using the approach introduced in Kublik et al. (2013) [7]. In this formulation, a boundary integral over a smooth, closed hypersurface is transformed into an equivalent volume integral defined in a sufficiently thin tubular neighborhood of the surface. The volumetric formulation makes it possible to use the simple trapezoidal rule on uniform Cartesian grids and relieves the need to use parameterization for developing quadrature. Consequently, typical point singularities in a layer potential extend along the surface's normal lines. We propose new higher-order corrections to the trapezoidal rule on the grid nodes around the singularities. This correction is based on local decompositions of the singularity and is dependent on the angle of approach to the singularity relative to the surface's principal curvature directions. The proposed decomposition, combined with the volumetric formulation, leads to a special quadrature error cancellation. (C)& nbsp;2022 The Author(s). Published by Elsevier Inc.
Keywords:
Level set methods
Closest point projection
Boundary integral formulations
Singular integrals
Trapezoidal rules
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.
Journal
IF:
3.8
Papers:
1.5W
Citations:
7.4W