High-order Adaptive Mesh Refinement multigrid Poisson solver in any dimension

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.(c) 2023 Elsevier Inc. All rights reserved.