Resolving the difficulty of T-junctions in Octree grids, Losasso et al.  introduced an ingenious Poisson solver with rectangular domains and Neumann boundary conditions. Its numerical solution was empirically observed  to be second order convergent and its numerical gradient was rigorously proved  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  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.
Bibliographical noteFunding Information:
The research of Byungjoon Lee was supported by NRF grant 2020R1A2C4002378 . The research of Jeongho Kim was supported by a grant from Kyung Hee University in 2022 ( KHU-20222220 ). The research of Chohong Min was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2019R1A6A1A11051177 and 2021R1A2C1095703 ).
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- Hodge decomposition
- Irregular domain
- Poisson equation