@article{9555106a7a9e4d0b9a2cdfd5c6c794ed,
title = "A smooth partition of unity finite element method for vortex particle regularization",
abstract = "We present a new class of C∞-smooth finite element spaces on Cartesian grids, based on a partition of unity approach. We use these spaces to construct smooth approximations of particle fields, i.e., finite sums of weighted Dirac deltas. In order to use the spaces on general domains, we propose a fictitious domain formulation, together with a new high-order accurate stabilization. Stability, convergence, and conservation properties of the scheme are established. Numerical experiments confirm the analysis and show that the Cartesian grid-size σ should be taken proportional to the square-root of the particle spacing h, resulting in significant speed-ups in vortex methods.",
keywords = "Biot-Savart law, Fictitious domains, Particle method, Partition of unity finite element method, Smooth shape functions, Vortex method",
author = "Matthias Kirchhart and Shinnosuke Obi",
note = "Funding Information: ∗Submitted to the journal{\textquoteright}s Methods and Algorithms for Scientific Computing section February 13, 2017; accepted for publication (in revised form) July 20, 2017; published electronically October 18, 2017. http://www.siam.org/journals/sisc/39-5/M111625.html Funding: The first author{\textquoteright}s work was supported by a MEXT scholarship of the Japanese Ministry of Education and the Keio Leading Edge Laboratory of Science and Technology, without which this research would have been impossible to conduct. †Department of Mechanical Engineering, Keio University, Yokohama, 223-8522 Japan (kirchhart@ keio.jp, obsn@mech.keio.ac.jp). Publisher Copyright: {\textcopyright} 2017 Matthias Kirchhart.",
year = "2017",
doi = "10.1137/17M1116258",
language = "English",
volume = "39",
pages = "A2345--A2364",
journal = "SIAM Journal on Scientific Computing",
issn = "1064-8275",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "5",
}