Multigrid approach in shifted linear systems for the non-degenerated twisted mass operator

TL;DR

This paper explores a multigrid solver strategy for shifted linear systems in twisted mass fermion simulations, introducing a novel initial guess method to improve computational efficiency in non-degenerate quark scenarios.

Contribution

It presents a new multigrid approach with a Lagrangian interpolation-based initial guess for shifted systems, enhancing simulation speed for non-degenerate twisted mass fermions.

Findings

Accelerates rational approximation in fermion simulations.

Effective initial guess strategy reduces computational time.

Applicable to $N_f=1+1$ and $N_f=2+1+1$ twisted mass sectors.

Abstract

Application of multigrid solvers in shifted linear systems is studied. We focus on accelerating the rational approximation needed for simulating single flavor operators. This is particularly useful, in the case of twisted mass fermions for mass non-degenerate quarks and can be employed to accelerate the $N_f=1+1$ sector of $N_f=2+1+1$ twisted mass fermion simulations. The multigrid solver is accelerated by employing suitable initial guesses. We propose a novel strategy for proposing initial guesses for shifted linear systems based on the Lagrangian interpolation of the previous solutions.