2010/01/18 by Mir Abbas Jalali · 12 citations
Mathematics · Physics and Astronomy · #Astronomy and Astrophysical Research #Classical mechanics #Finite element method #Galaxies: Formation, Evolution, Phenomena #Galerkin method #Geometry #Gravitation #Gravitational potential #Mathematical analysis #Mathematics #Mechanics #Phase space #Physics #Quadratic equation #Quantum mechanics #Rotational symmetry #Stellar, planetary, and galactic studies #astro-ph.GA #astro-ph.IM
paper · pdf · doi:10.1111/j.1365-2966.2010.16365.x
published in Monthly Notices of the Royal Astronomical Society (Oxford University Press) · 11 pages, three figures, accepted for publication by MNRAS
arxiv created 2010/01/18 · openalex publication_date 2010/03/01 · arxiv updated 2015/05/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
I formulate a general finite element method (FEM) for self-gravitating stellar systems. I split the configuration space to finite elements, and express the potential and density functions over each element in terms of their nodal values and suitable interpolating functions. General expressions are then introduced for the Hamiltonian and phase-space distribution functions of the stars that visit a given element. Using the weighted residual form of Poisson's equation, I derive the Galerkin projection of the perturbed collisionless Boltzmann equation, and assemble the global evolutionary equations of nodal distribution functions. The FEM is highly adaptable to all kinds of potential and density profiles, and it can deal with density clumps and initially non-axisymmetric systems. I use ring elements of non-uniform widths, choose linear and quadratic interpolation functions in the radial direction, and apply the FEM to the stability analysis of the cutout Mestel disc. I also integrate the forced evolutionary equations and investigate the disturbances of a stable stellar disc due to the gravitational field of a distant satellite galaxy. The performance of the FEM and its prospects are discussed.