期刊論文
| 學年 | 113 |
|---|---|
| 學期 | 2 |
| 出版（發表）日期 | 2025-04-18 |
| 作品名稱 | Enhanced Efficient 3D Poisson Solver Supporting Dirichlet, Neumann, and Periodic Boundary Conditions. |
| 作品名稱（其他語言） | |
| 著者 | Chieh-Hsun Wu |
| 單位 | |
| 出版者 | |
| 著錄名稱、卷期、頁數 | Computation 13(4), p.99 |
| 摘要 | This paper generalizes the efficient matrix decomposition method for solving the finite-difference (FD) discretized three-dimensional (3D) Poisson’s 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—though 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. |
| 關鍵字 | three-dimension; Poisson’s equation; finite difference; matrix decomposition; boundary conditions; Fourier analysis |
| 語言 | en |
| ISSN | 2079-3197 |
| 期刊性質 | 國外 |
| 收錄於 | ESCI |
| 產學合作 | |
| 通訊作者 | |
| 審稿制度 | 否 |
| 國別 | CHE |
| 公開徵稿 | |
| 出版型式 | ,電子版 |
| 相關連結 |
機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/127797 ) |