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Sci. Comput."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>We present a new algorithm for the automatic one-shot generation of scattered node sets on irregular two dimensional (2D) and three dimensional (3D) domains using Poisson disk sampling coupled to novel parameter-free, high-order parametric spherical-radial-basis-function-based geometric modeling of irregular domain boundaries. Our algorithm also automatically modifies the scattered node sets locally for time-varying embedded boundaries in the domain interior. We derive complexity estimates for our node generator in 2 and 3 dimensions that establish its scalability, and verify these estimates with timing experiments. We explore the influence of Poisson disk sampling parameters on both quasi-uniformity in the node sets and errors in a radial-basis-function-based--finite-difference discretization of the heat equation. In all cases, our framework requires only a small number of \u201cseed\u201d nodes on domain boundaries. The entire framework exhibits $O(N)$ complexity in both 2 and 3 dimensions.<\/jats:p>","DOI":"10.1137\/17m114090x","type":"journal-article","created":{"date-parts":[[2018,8,21]],"date-time":"2018-08-21T12:26:46Z","timestamp":1534854406000},"page":"A2584-A2608","source":"Crossref","is-referenced-by-count":41,"title":["Robust Node Generation for Mesh-free Discretizations on Irregular Domains and Surfaces"],"prefix":"10.1137","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4987-2972","authenticated-orcid":true,"given":"Varun","family":"Shankar","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert M.","family":"Kirby","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Aaron L.","family":"Fogelson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,8,21]]},"reference":[{"key":"atypb1","unstructured":"G. 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