A level set approach for computing solutions to incompressible two-phase flow
Journal of Computational Physics
Multigrid methods for N-body gravitational systems
Journal of Computational Physics
On recombining iterants in multigrid algorithms and problems with small islands
SIAM Journal on Scientific Computing
A Cartesian Grid Projection Method for the Incompressible Euler Equations in Complex Geometries
SIAM Journal on Scientific Computing
A Cartesian grid embedded boundary method for Poisson's equation on irregular domains
Journal of Computational Physics
An adaptive level set approach for incompressible two-phase flows
Journal of Computational Physics
A fast adaptive multipole algorithm in three dimensions
Journal of Computational Physics
An accurate Cartesian grid method for viscous incompressible flows with complex immersed boundaries
Journal of Computational Physics
A Fast Direct Solver for Elliptic Partial Differential Equations on Adaptively Refined Meshes
SIAM Journal on Scientific Computing
A boundary condition capturing method for Poisson's equation on irregular domains
Journal of Computational Physics
A cell-centered adaptive projection method for the incompressible Euler equations
Journal of Computational Physics
A Cartesian grid embedded boundary method for the heat equation on irregular domains
Journal of Computational Physics
Level set methods: an overview and some recent results
Journal of Computational Physics
A second-order-accurate symmetric discretization of the Poisson equation on irregular domains
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Block structured adaptive mesh and time refinement for hybrid, hyperbolic+N-body systems
Journal of Computational Physics
First-ever full observable universe simulation
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Hi-index | 31.45 |
We present a new multigrid scheme for solving the Poisson equation with Dirichlet boundary conditions on a Cartesian grid with irregular domain boundaries. This scheme was developed in the context of the Adaptive Mesh Refinement (AMR) schemes based on a graded-octree data structure. The Poisson equation is solved on a level-by-level basis, using a ''one-way interface'' scheme in which boundary conditions are interpolated from the previous coarser level solution. Such a scheme is particularly well suited for self-gravitating astrophysical flows requiring an adaptive time stepping strategy. By constructing a multigrid hierarchy covering the active cells of each AMR level, we have designed a memory-efficient algorithm that can benefit fully from the multigrid acceleration. We present a simple method for capturing the boundary conditions across the multigrid hierarchy, based on a second-order accurate reconstruction of the boundaries of the multigrid levels. In case of very complex boundaries, small scale features become smaller than the discretization cell size of coarse multigrid levels and convergence problems arise. We propose a simple solution to address these issues. Using our scheme, the convergence rate usually depends on the grid size for complex grids, but good linear convergence is maintained. The proposed method was successfully implemented on distributed memory architectures in the RAMSES code, for which we present and discuss convergence and accuracy properties as well as timing performances.