Multigrid on Composite Meshes

Abstract

Abstract. The multigrid method is applied to the numerical solution of elliptic equations on general composite overlapping meshes. Computational results show that good convergence rates are obtained.

Local Bisection Refinement for N-Simplicial Grids Generated by Reflection

“…This means that the method can also be used for grids which have to fit curved boundaries, especially because the new method allows one to move the vertices of the grid. Finally, one can also cover regions with component grids of type G, as is done for n-cube type grids by Henshaw and Chesshire in [17].…”

Schwarz domain decomposition for the incompressible Navier-Stokes equations in general co-ordinates

“…This, as explained above, requires that the compatibility condition (24) is satisfied for the subdomains. To satisfy (24), the authors correct the boundary mass fluxes using the MIC scheme. As they observe, the applied corrections are relatively small (less than 1%, see [29]).…”

“…An explicit time integration scheme is used, so that only a domain decomposition problem for the pressure equation remains. In [24], a multi-grid method is used to solve the Poisson equation on arbitrary overlapping composite grids, and good convergence results are obtained. A complete composite multi-grid (CCMG) method is used where information is transferred between subdomains at each grid level.…”

“…A complete composite multi-grid (CCMG) method is used where information is transferred between subdomains at each grid level. In [25], the procedures described in [23,24] are extended by considering Neumann -Dirichlet coupling conditions instead of the basic Schwarz iteration.…”

“…In [28,29], an explicit time integration was used like in [23], but with an extension to arbitrary overlapping grids, thus releasing the requirement of having coincident grid points at the inter-grid boundaries. In contrast to Reference [24], References [28 -30] employ an incomplete composite multi-grid (ICMG) method where information is transferred between subdomains only at the finest grid level. The reason is that ICMG is much easier to implement than CCMG and also appears to be efficient.…”