A Reduced Coupling-Space Multigrid Schur Preconditioner for Fictitious-Domain Interface Problems

We study a reduced multigrid Schur preconditioner for the fictitious-domain method with distributed Lagrange multipliers applied to elliptic interface problems. The method replaces the costly background solve by a multigrid approximation and treats the resulting correction only in the multiplier coupling space through a Woodbury formula. Numerical experiments show a marked improvement over the baseline preconditioner and consistently rapid convergence under mesh refinement and coefficient contrast.