A multigrid method for CutFEM and its implementation on GPU

Fuente: arXiv
Saved in:
Bibliographic Details
Main Authors: Cui, Cu, Kanschat, Guido
Format: Preprint
Published: 2025
Subjects:
Online Access:
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866909738109763584
author Cui, Cu
Kanschat, Guido
author_facet Cui, Cu
Kanschat, Guido
contents We present a multigrid method for an unfitted finite element discretization of the Dirichlet boundary value problem. The discretization employs Nitsche's method to implement the boundary condition and additional face based ghost penalties for stabilization. We apply standard intergrid operators, relying on the fact that the relevant domain of computation does not grow under mesh refinement. The smoother is a parallel implementation of the multiplicative vertex-patch smoother with inconsistent treatment of ghost penalties. Our computational results show that we obtain a fast converging method. Furthermore, runtime comparison to fitted methods show that the losses are moderate although many optimizations for Cartesian vertex patches cannot be applied on cut patches.
format Preprint
id arxiv_https___arxiv_org_abs_2508_11608
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A multigrid method for CutFEM and its implementation on GPU
Cui, Cu
Kanschat, Guido
Numerical Analysis
65N55, 65Y05, 65Y10
We present a multigrid method for an unfitted finite element discretization of the Dirichlet boundary value problem. The discretization employs Nitsche's method to implement the boundary condition and additional face based ghost penalties for stabilization. We apply standard intergrid operators, relying on the fact that the relevant domain of computation does not grow under mesh refinement. The smoother is a parallel implementation of the multiplicative vertex-patch smoother with inconsistent treatment of ghost penalties. Our computational results show that we obtain a fast converging method. Furthermore, runtime comparison to fitted methods show that the losses are moderate although many optimizations for Cartesian vertex patches cannot be applied on cut patches.
title A multigrid method for CutFEM and its implementation on GPU
topic Numerical Analysis
65N55, 65Y05, 65Y10
url https://arxiv.org/abs/2508.11608