Implementation of Simultaneous Inversion of a Multi-shifted Dirac Matrix for Twisted-Mass Fermions within DD-{\alpha}AMG

TL;DR

This paper presents an implementation of simultaneous multi-shifted Dirac matrix inversion for twisted-mass fermions using adaptive algebraic multigrid methods, improving efficiency for lattice QCD simulations at physical quark masses.

Contribution

The authors develop and implement a novel approach for simultaneous inversion of Dirac matrices with multiple right-hand sides and shifts within the DD-αAMG framework, enhancing computational performance.

Findings

Demonstrated scalability of the implementation.

Compared different Block-Krylov solver techniques.

Achieved improved inversion efficiency at physical quark masses.

Abstract

At physical light quark masses, efficient linear solvers are crucial for carrying out the millions of inversions of the Dirac matrix required for obtaining high statistics in quark correlation functions. Adaptive algebraic multi-grid methods have proven to be very efficient in such cases, exhibiting mild critical slowing down towards very light quark masses and outperforming traditional solver methods, such as the conjugate gradient method, at the physical point. We will discuss our implementations of simultaneous inversion of a (degenerate) Dirac matrix for twisted-mass fermions for multiple right-hand-sides (rhs) with multi-shifts and block-Krylov solvers. The implementation is carried out within the community library DD$\alpha$AMG, which implements aggregation-based Domain Decomposition adaptive algebraic multi-grid methods. The block-Krylov solvers are provided via the Fast Accurate Block Linear krylOv Solver (Fabulous) library and can be used at coarser levels. Our code inverts Dirac matrices with different twisted-mass terms and for multiple rhs simultaneously and is thus also suitable for components within a typical lattice QCD simulation workflow, such as the rational approximation. We show preliminary results on scalability and compare the performance of our implementation when using different Block-Krylov solver techniques.