@article{57bedfcdc4b44037ac1c2f541b65d6fa,
title = "A fast boundary integral method for high-order multiscale mesh generation",
abstract = "In this work we present an algorithm to construct an infinitely differentiable smooth surface from an input consisting of a (rectilinear) triangulation of a surface of arbitrary shape. The original surface can have nontrivial genus and multiscale features, and our algorithm has computational complexity which is linear in the number of input triangles. We use a smoothing kernel to define a function Φ whose level set defines the surface of interest. Charts are subsequently generated as maps from the original user-specified triangles to R3. The degree of smoothness is controlled locally by the kernel to be commensurate with the fineness of the input triangulation. The expression for Φ can be transformed into a boundary integral, whose evaluation can be accelerated using a fast multipole method. We demonstrate the effectiveness and cost of the algorithm with polyhedral and quadratic skeleton surfaces obtained from computer-aided design and meshing software.",
keywords = "Boundary integral, Fast multipole method, High-order surface discretization, Level set, Mesh generation",
author = "Felipe Vico and Leslie Greengard and Michael O'Neil and Manas Rachh",
note = "Funding Information: \ast Submitted to the journal's Methods and Algorithms for Scientific Computing section September 30, 2019; accepted for publication February 25, 2020; published electronically April 27, 2020. https://doi.org/10.1137/19M1290450 \bfF \bfu \bfn \bfd \bfi \bfn \bfg : This work was supported by the Office of Naval Research through grant N00014-18-1-2307. The work of the third author was supported by the Office of Naval Research under grants N00014-17-1-2059 and N00014-17-1-2451. \dagger Instituto de Telecomunicaciones y Aplicaciones Multimedia (ITEAM), Universidad Polit\{\`e}cnica de Val\{\`e}ncia, Val\{\`e}ncia, Spain 46022 (
[email protected]). \ddagger Courant Institute, Center for Computational Mathematics, New York University, Flatiron Institute, New York, NY 10012 (
[email protected]). \S Corresponding author. Courant Institute, New York University, New York, NY 10012 (oneil@ cims.nyu.edu). \P Center for Computational Mathematics, Flatiron Institute, New York, NY 10010 (mrachh@ flatironinstitute.org). Publisher Copyright: {\textcopyright} 2020 Society for Industrial and Applied Mathematics.",
year = "2020",
doi = "10.1137/19M1290450",
language = "English (US)",
volume = "42",
pages = "A1380--A1401",
journal = "SIAM Journal on Scientific Computing",
issn = "1064-8275",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "2",
}