A further study of the solution of Poisson's equation for three-dimensional spiral galaxies

1986 ◽  
Vol 10 (2) ◽  
pp. 162-167
Author(s):  
Hong-guang Bi ◽  
Qiu-he Peng ◽  
Zong-yun Li
Keyword(s):  
Spiral Galaxies ◽  
Three Dimensional ◽  
Poisson’S Equation ◽  
Poisson's Equation

scholarly journals A Family of Sixth-Order Compact Finite-Difference Schemes for the Three-Dimensional Poisson Equation

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Yaw Kyei ◽  
John Paul Roop ◽  
Guoqing Tang
Keyword(s):  
Finite Difference ◽  
High Performance ◽  
Three Dimensional ◽  
Difference Schemes ◽  
Poisson’S Equation ◽  
Sixth Order ◽  
Finite Difference Schemes ◽  
Poisson's Equation ◽  
Compact Finite Difference ◽  
Compact Finite Difference Schemes

We derive a family of sixth-order compact finite-difference schemes for the three-dimensional Poisson's equation. As opposed to other research regarding higher-order compact difference schemes, our approach includes consideration of the discretization of the source function on a compact finite-difference stencil. The schemes derived approximate the solution to Poisson's equation on a compact stencil, and thus the schemes can be easily implemented and resulting linear systems are solved in a high-performance computing environment. The resulting discretization is a one-parameter family of finite-difference schemes which may be further optimized for accuracy and stability. Computational experiments are implemented which illustrate the theoretically demonstrated truncation errors.

A High-Accuracy Mechanical Quadrature Method for Solving the Axisymmetric Poisson's Equation

2017 ◽  
Vol 9 (2) ◽  
pp. 393-406 ◽  
Author(s):  
Hu Li ◽  
Jin Huang
Keyword(s):  
Three Dimensional ◽  
High Accuracy ◽  
Poisson’S Equation ◽  
Two Dimensional ◽  
Quadrature Method ◽  
Poisson's Equation ◽  
Mechanical Quadrature ◽  
Asymptotic Error ◽  
Accuracy Order ◽  
Mechanical Quadrature Method

AbstractIn this article, we consider the numerical solution for Poisson's equation in axisymmetric geometry. When the boundary condition and source term are axisymmetric, the problem reduces to solving Poisson's equation in cylindrical coordinates in the two-dimensional (r,z) region of the original three-dimensional domain S. Hence, the original boundary value problem is reduced to a two-dimensional one. To make use of the Mechanical quadrature method (MQM), it is necessary to calculate a particular solution, which can be subtracted off, so that MQM can be used to solve the resulting Laplace problem, which possesses high accuracy order and low computing complexities. Moreover, the multivariate asymptotic error expansion of MQM accompanied with for all mesh widths hi is got. Hence, once discrete equations with coarse meshes are solved in parallel, the higher accuracy order of numerical approximations can be at least by the splitting extrapolation algorithm (SEA). Meanwhile, a posteriori asymptotic error estimate is derived, which can be used to construct self-adaptive algorithms. The numerical examples support our theoretical analysis.

scholarly journals Efficient and accurate solver of the three-dimensional screened and unscreened Poisson's equation with generic boundary conditions

2012 ◽  
Vol 137 (13) ◽  
pp. 134108 ◽  
Author(s):  
Alessandro Cerioni ◽  
Luigi Genovese ◽  
Alessandro Mirone ◽  
Vicente Armando Sole
Keyword(s):  
Boundary Conditions ◽  
Three Dimensional ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
Generic Boundary

scholarly journals Domain decomposition based on a direct method for solving the three-dimensional Poisson's equation in nonstationary astrophysical problems

2015 ◽  
pp. 94-98
Author(s):  
Н.В. Снытников
Keyword(s):  
Dirichlet Problem ◽  
Parallel Algorithm ◽  
Direct Method ◽  
Three Dimensional ◽  
Poisson’S Equation ◽  
Variable Separation ◽  
Poisson's Equation ◽  
Academy Of Sciences ◽  
Variable Separation Method ◽  
A Direct Method

Предложен новый параллельный алгоритм для решения трехмерного уравнения Пуассона в контексте нестационарных задач астрофизики. Алгоритм основан на декомпозиции трехмерной области по двум направлениям, в применении прямого метода решения задачи Дирихле в каждой подобласти и в комбинации метода сопряжения подобластей для двумерного экранированного уравнения Пуассона с методом разделения переменных. Тестовые эксперименты проводились на суперкомпьютерах Межведомственного суперкомпьютерного центра (МСКЦ) и Сибирского суперкомпьютерного центра (ССКЦ). A new parallel algorithm for solving the three-dimensional Poisson's equation in the context of nonstationary problems of astrophysics is proposed. This algorithm is based on a decomposition of the 3D domain in two directions, on the application of a direct method for solving the Dirichlet problem in each subdomain, and on a combination of subdomains coupling for the screened Poisson's equation with the variable separation method. Test experiments were conducted on supercomputers installed at the Joint Supercomputing Center of Russian Academy of Sciences (Moscow) and at the Siberian Supercomputing Center (Novosibirsk).

scholarly journals Potential-Density Basis Sets for Three-Dimensional Disks

1996 ◽  
Vol 169 ◽  
pp. 509-510
Author(s):  
David J.D. Earn
Keyword(s):  
Density Function ◽  
Potential Function ◽  
Three Dimensional ◽  
Poisson’S Equation ◽  
Basis Sets ◽  
Poisson's Equation ◽  
Potential Density ◽  
Expansion Coefficients

Poisson's equation, ∇2ψ = 4πGρ, can be solved approximately using basis sets of potential-density pairs. A given density is approximated by a truncated expansion; the computed expansion coefficients immediately yield the corresponding potential since each basis density function is paired with a basis potential function, and Poisson's equation is linear.

scholarly journals Distributed Algorithms for Three-dimensional Semiconductor Device Simulations

VLSI Design ◽  
1998 ◽  
Vol 6 (1-4) ◽  
pp. 123-126
Author(s):  
Mei-Kei Ieong ◽  
Ting-Wei Tang
Keyword(s):  
Distributed Algorithms ◽  
Message Passing ◽  
Semiconductor Device ◽  
Three Dimensional ◽  
Iterative Algorithms ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
Network Of Workstations

We describe a newly developed parallel three-dimensional semiconductor device simulator. The program utilizes the message passing architecture and has been developed on a network of workstations. Two iterative algorithms to solve the nonlinear semiconductor device equations are presented. The algorithms are tested by simulating a three-dimensional MOSFET structure. A near-ideal speedup for the distributed algorithms has been obtained for Poisson’s equation.

Sign in / Sign up

Export Citation Format

Share Document