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We present a generalized algorithm based on a spherical harmonics expansionmethod for efficient computation of the three-dimensional gravitationalpotential on a multi-patch grid in spherical geometry. Instead of solving forthe gravitational potential by superposition of separate contributions from themass density distribution on individual grid patch our new algorithm computesdirectly the gravitational potential due to contributions from all grid patchesin one computation step, thereby reducing the computational cost of the gravitysolver. This is possible by considering a set of angular weights which arederived from rotations of spherical harmonics functions defined in a globalcoordinate system that is common for all grid patches. Additionally, ouralgorithm minimizes data communication between parallel compute tasks byeliminating its proportionality to the number of subdomains in the gridconfiguration, making it suitable for parallelized computation on a multi-patchgrid configuration with any number of subdomains. Test calculations of thegravitational potential of a tri-axial ellipsoidal body with constant massdensity on the Yin-Yang two-patch overset grid demonstrate that our methoddelivers the same level of accuracy as a previous method developed for theYin-Yang grid, while offering improved computation efficiency and parallelscaling behaviour.

astrophysical journal/the astrophysical journal

A Generalized Solution Method for Parallelized Computation of the  Three-dimensional Gravitational Potential on a Multi-patch grid in Spherical  Geometry