• Journal of applied mathematics & informatics
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• 제6권1호
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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 applied mathematics & informatics
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• 제8권1호
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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.

• 한국정보처리학회논문지
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• 제4권3호
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• pp.720-730
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• 1997

본 연구에서는 격자점의 갯수나 경계 조건에 관계없이 포아송 방정식을 푸는 일반적인 프로그램을 개발하고, 수퍼 컴퓨터의 병렬 기능과 벡터 기능을 이용하여 이 프로그램 을 고속화시켰다.우리는 실제 현압에 사용되고 있는 바로토로픽 예측 모델을 이용하여 실제 태풍인 Elena의 궤도를 예측하여 보았고, 병렬화된 고속의 포아송 방정식을 사용하는 경우 상당한 시간이 절약됨을 알 수 있었다. 72시간 후의 허리케인의 궤도 예측을 시도하였다. 3000여개의 격자점 위에서 시간 간격을 16분으로 하여 실험하였는데 8개 벡터 프로세서를 갖고 있는 Aliant FX/8에서 30초만에 이루어 졌고, 3.7의 계산 효율 을 얻어냈다.

• 천문학회보
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• 제44권1호
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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.