Abstract
A numerical method to solve the d-dimensional Poisson equation with 2pth-order accuracy for arbitrary d and p integers is proposed in the Adaptive Mesh Refinement framework. Compact finite differences provide high-order compact stencils fitted for the AMR framework where reaching far-away neighboring points is very penalizing. Vertex-centered mesh refinement and interpolation ease the implementation of a multigrid algorithm formulated in the general case for any stencil in any dimension. Its computational costs are compared to those of other existing methods. And, in extensive numerical experiments, a sixth-order version of it in dimensions two to six and a tenth-order version in dimension three are tested.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
