Abstract
Self-gravity and rotation are two key ingredients in dynamics of astronomical disk systems such as galactic and protostellar disks. Despite its importance, there has not yet been so far an efficient algorithm to solve the Poisson equation in three-dimensional cylindrical coordinates under vacuum boundary conditions. By generalizing the James algorithm to cylindrical coordinates, we develop an accurate (second-order convergence) and efficient (faster than MHD) cylindrical Poisson solver that is scalable up to ∼ 104 cores. We develop a method to calculate the cylindrical discrete Green’s function, which is an essential element of the James algorithm to estabilish its second-order accuracy. We implement our cylindrical version of the James algorithm in Athena++ code and demonstrate its accuracy and efficiency by performing the convergence test and the weak scaling test.
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