A parallel fictitious domain multigrid preconditioner for the solution of Poisson’s equation in complex geometries |
| |
| Affiliation: | 1. Division of Fluid and Experimental Mechanics, Department of Engineering Sciences and Mathematics, Luleå University of Technology, Sweden;2. Department of Mechanical and Industrial Engineering, Indian Institute of Technology, Roorkee, India;3. Division of Fluid and Experimental Mechanics, Department of Engineering Sciences and Mathematics, Luleå University of Technology, Sweden;4. Department of Mechanical and Industrial Engineering, Indian Institute of Technology, Roorkee, India;5. Water Power Laboratory, Department of Energy and Process Engineering, Norwegian University of Science and Technology, Norway;1. Institute of Applied Mathematics (LS III), TU Dortmund University, Vogelpothsweg 87, D-44227 Dortmund, Germany;2. Alfred Wegener Institute, Helmholtz Center for Polar and Marine Research, Am Handelshafen 12, D-27570 Bremerhaven, Germany;3. Applied Mathematics 1, University Erlangen-Nuremberg, Cauerstr. 11, D-91058 Erlangen, Germany;1. Department of Mathematics, University of North Carolina, Chapel Hill, NC, United States of America;2. Departments of Mathematics, Applied Physical Sciences, and Biomedical Engineering, University of North Carolina, Chapel Hill, NC, United States of America;1. Department of Flow and Material Simulation, Fraunhofer Institute of Industrial Mathematics ITWM, Germany;2. Department of Applied Mechanics, University of Kaiserslautern, Germany |
| |
| Abstract: | A parallel multilevel preconditioner based on domain decomposition and fictitious domain methods has been presented for the solution of the Poisson equation in complicated geometries. Rectangular blocks with matching grids on interfaces on a structured rectangular mesh have been used for the decomposition of the problem domain. Sloping sides or curved boundary surfaces are approximated using stepwise surfaces formed by the grid cells. A seven-point stencil based on the central difference scheme has been used for the discretization of the Laplacian for both interior and boundary grid points, and this results in a symmetric linear algebraic system for any type of boundary condition. The preconditioned conjugate gradient method has been used for the solution of this symmetric system. The multilevel preconditioner for the CG is based on a V-cycle multigrid applied to the Poisson equation on a fictitious domain formed by the union of the rectangular blocks used for the domain decomposition. Numerical results are presented for two typical Poisson problems in complicated geometries—one related to heat conduction, and the other one arising from the LES/DNS of incompressible turbulent flow over a packed array of spheres. These results clearly show the efficiency and robustness of the proposed approach. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
