• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.65-78
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• 1999

We present a fast/parallel Poisson solver on disks, based on efficient evaluation of the exact solution given by the Newtonian potential and the Poisson integral. Derived from an integral formula-tion it is more accurate and simpler in parallel implementation and in upgrading to a higher order algorithm than an algorithm which solves the linear system obtained from a differential formulation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.1
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• pp.27-39
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• 1998

We describe a fast numerical method for non-separable elliptic equations in self-adjoin form on irregular adaptive domains. One of the most successful results in numerical PDE is developing rapid elliptic solvers for separable EPDEs, for example, Fourier transformation methods for Poisson problem on a square, however, it is known that there is no rapid elliptic solvers capable of solving a general nonseparable problems. It is the purpose of this paper to present an iterative solver for linear EPDEs in self-adjoint form. The scheme discussed in this paper solves a given non-separable equation using a sequence of solutions of Poisson equations, therefore, the most important key for such a method is having a good Poison solver. High performance is achieved by using a fast high-order adaptive Poisson solver which requires only about 500 floating point operations per gridpoint in order to obtain machine precision for both the computed solution and its partial derivatives. A few numerical examples have been presented.

• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.27-44
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• 2001

A fast Poisson solver on irregular domains, based on bound-ary methods, is presented. The harmonic polynomial approximation of the solution of the associated homogeneous problem provides a good practical boundary method which allows a trivial parallel processing for solution evaluation or straightfoward computations of the interface values for domain decomposition/embedding. AMS Mathematics Subject Classification : 65N35, 65N55, 65Y05.

• The Transactions of the Korea Information Processing Society
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• v.4 no.3
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• pp.720-730
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• 1997

In this paper, we develp the code, called the fast parallel Poisson solver, which solves the poisson's equation of arbitraty dimension and parallelize it, And we apply the fast parallel poisson solver to the barotopic predic-tion model to explore the advantages of using it.In particular, we apply this model to the track forecasting of hurricane time required to integrate the barotropic model.A 72-h track prdeiciton was made by using time step of 16 minutes on a network of about 3000 grid points.The prediction 30 seconds on the 8-processor Alliant FX/8 mini supercomputer.It was a speed-up of 3.7 wen compared to the one-processor version.

• The Bulletin of The Korean Astronomical Society
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• v.44 no.1
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• pp.46.1-46.1
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• 2019

We present an accurate and efficient method to calculate the gravitational potential of an isolated system in three-dimensional Cartesian and cylindrical coordinates subject to vacuum (open) boundary conditions. Our method consists of two parts: an interior solver and a boundary solver. The interior solver adopts an eigenfunction expansion method together with a tridiagonal matrix solver to solve the Poisson equation subject to the zero boundary condition. The boundary solver employs James's method to calculate the boundary potential due to the screening charges required to keep the zero boundary condition for the interior solver. A full computation of gravitational potential requires running the interior solver twice and the boundary solver once. We develop a method to compute the discrete Green's function in cylindrical coordinates, which is an integral part of the James algorithm to maintain second-order accuracy. We implement our method in the {\tt Athena++} magnetohydrodynamics code, and perform various tests to check that our solver is second-order accurate and exhibits good parallel performance.