{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:10:53Z","timestamp":1760058653216,"version":"build-2065373602"},"reference-count":39,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,18]],"date-time":"2025-04-18T00:00:00Z","timestamp":1744934400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science and Technology Council (NSTC) in Taiwan","award":["NSTC-112-2221-E-032-008"],"award-info":[{"award-number":["NSTC-112-2221-E-032-008"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>This paper generalizes the efficient matrix decomposition method for solving the finite-difference (FD) discretized three-dimensional (3D) Poisson\u2019s equation using symmetric 27-point, 4th-order accurate stencils to adapt more boundary conditions (BCs), i.e., Dirichlet, Neumann, and Periodic BCs. It employs equivalent Dirichlet nodes to streamline source term computation due to BCs. A generalized eigenvalue formulation is presented to accommodate the flexible 4th-order stencil weights. The proposed method significantly enhances computational speed by reducing the 3D problem to a set of independent 1D problems. As compared to the typical matrix inversion technique, it results in a speed-up ratio proportional to n4, where n is the number of nodes along one side of the cubic domain. Accuracy is validated using Gaussian and sinusoidal source fields, showing 4th-order convergence for Dirichlet and Periodic boundaries, and 2nd-order convergence for Neumann boundaries due to extrapolation limitations\u2014though with lower errors than traditional 2nd-order schemes. The method is also applied to vortex-in-cell flow simulations, demonstrating its capability to handle outer boundaries efficiently and its compatibility with immersed boundary techniques for internal solid obstacles.<\/jats:p>","DOI":"10.3390\/computation13040099","type":"journal-article","created":{"date-parts":[[2025,4,18]],"date-time":"2025-04-18T08:24:07Z","timestamp":1744964647000},"page":"99","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Enhanced Efficient 3D Poisson Solver Supporting Dirichlet, Neumann, and Periodic Boundary Conditions"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1317-7254","authenticated-orcid":false,"given":"Chieh-Hsun","family":"Wu","sequence":"first","affiliation":[{"name":"Department of Civil Engineering, Tamkang University, New Taipei City 251301, Taiwan"}]}],"member":"1968","published-online":{"date-parts":[[2025,4,18]]},"reference":[{"key":"ref_1","unstructured":"Zhong, Y., Shirinzadeh, B., Alici, G., and Smith, J. 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