A Hybrid DST-Accelerated Finite-Difference Solver for 2D and 3D Poisson Equations with Dirichlet Boundary Conditions
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| Publicado en: | Mathematics vol. 13, no. 17 (2025), p. 2776-2793 |
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| Autor principal: | |
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MDPI AG
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| Acceso en línea: | Citation/Abstract Full Text + Graphics Full Text - PDF |
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| 022 | |a 2227-7390 | ||
| 024 | 7 | |a 10.3390/math13172776 |2 doi | |
| 035 | |a 3249691809 | ||
| 045 | 2 | |b d20250101 |b d20251231 | |
| 084 | |a 231533 |2 nlm | ||
| 100 | 1 | |a Pei Jing | |
| 245 | 1 | |a A Hybrid DST-Accelerated Finite-Difference Solver for 2D and 3D Poisson Equations with Dirichlet Boundary Conditions | |
| 260 | |b MDPI AG |c 2025 | ||
| 513 | |a Journal Article | ||
| 520 | 3 | |a Finite-difference methods are widely used to solve partial differential equations in diverse practical applications. Despite their prevalence, the computational efficiency of these methods encounters limitations due to the need to solve linear equation systems through matrix inversion or iterative solver, which is particularly challenging in scenarios involving high dimensions. The demand for numerical methods with high accuracy and fast computational speed is steadily increasing. To address this challenge, we present an efficient and accurate algorithm for high-dimensional numerical modeling. This approach combines a central finite-difference method with the discrete Sine transform (DST) scheme to solve the Poisson equation under Dirichlet boundary conditions (DBCs). To balance numerical accuracy and computation, the DST scheme is applied along one direction in the 2D case and two directions in the 3D case. This strategy effectively reduces problem complexity while maintaining low computational cost. The hybrid DST-accelerated finite-difference approach substantially lowers the computational cost associated with solving the Poisson equation on large grids. Comprehensive numerical experiments for 2D and 3D Poisson equations with DBCs have been conducted. The obtained numerical results demonstrate that the proposed hybrid method not only significantly reduces the computational expenses, but also maintains the central finite-difference accuracy. | |
| 653 | |a Accuracy | ||
| 653 | |a Partial differential equations | ||
| 653 | |a Mathematical analysis | ||
| 653 | |a Fourier transforms | ||
| 653 | |a Numerical models | ||
| 653 | |a Finite difference method | ||
| 653 | |a Computational efficiency | ||
| 653 | |a Boundary conditions | ||
| 653 | |a Computing costs | ||
| 653 | |a Numerical analysis | ||
| 653 | |a Solvers | ||
| 653 | |a Linear equations | ||
| 653 | |a Methods | ||
| 653 | |a Algorithms | ||
| 653 | |a Numerical methods | ||
| 653 | |a Boundary value problems | ||
| 653 | |a Efficiency | ||
| 653 | |a Poisson equation | ||
| 700 | 1 | |a Tong Xiaozhong | |
| 773 | 0 | |t Mathematics |g vol. 13, no. 17 (2025), p. 2776-2793 | |
| 786 | 0 | |d ProQuest |t Engineering Database | |
| 856 | 4 | 1 | |3 Citation/Abstract |u https://www.proquest.com/docview/3249691809/abstract/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text + Graphics |u https://www.proquest.com/docview/3249691809/fulltextwithgraphics/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |
| 856 | 4 | 0 | |3 Full Text - PDF |u https://www.proquest.com/docview/3249691809/fulltextPDF/embedded/7BTGNMKEMPT1V9Z2?source=fedsrch |