A super-convergence analysis of the Poisson solver with Octree grids and irregular domains
- 주제(키워드) Hodge decomposition , Irregular domain , Octree , Poisson equation , Super-convergence
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 Academic Press Inc.
- 발행년도 2023
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000208998
- 본문언어 영어
- Published As https://doi.org/10.1016/j.jcp.2023.112212
초록/요약
Resolving the difficulty of T-junctions in Octree grids, Losasso et al. [9] introduced an ingenious Poisson solver with rectangular domains and Neumann boundary conditions. Its numerical solution was empirically observed [9] to be second order convergent and its numerical gradient was rigorously proved [8] to be one and a half order convergent, which is the so-called super-convergence. This article is devoted to extending the Poisson solver and its supporting proof from rectangular to irregular domains. The generalized Whitney decomposition [12] efficiently generates octree grids for irregular domains imposing the finest resolution near the boundary of domain. Combined with the Heaviside treatment [17,4], the Poisson solver is extended to irregular domains and a novel and rigorous analysis shows that the aforementioned super-convergence still holds true. © 2023 Elsevier Inc.
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