Multigrid Methods for Self-Gravity in the Collapse of Molecular Clouds

Abstract

The magnetohydrodynamics of gravitational collapse in molecular clouds has been extensively studied in recent years, particularly thanks to ever-increasing computational resources. We wish to develop a module that will be effective for solving self-gravity (a special case of Poisson’s equation) using a combination of two complementary numerical techniques: multigrid and nested grid methods. In this paper, we will first motivate the importance of accurate calculation of self-gravity for collapse and star formation. We will then proceed to discuss ways that multigrid and nested grid methods can be integrated to create an algorithm that is both efficient and sufficiently accurate.