Hierarchically deflated conjugate residual

Abstract

We present a progress report on a new class of multigrid solver algorithm suitable for the solution of 5d chiral fermions such as Domain Wall fermions and the Continued Fraction overlap. Unlike HDCG \cite{Boyle:2014rwa}, the algorithm works directly on a nearest neighbour fine operator. The fine operator used is Hermitian indefinite, for example ${\Gamma }_5{D}_{dwf}$, and convergence is achieved with an indefinite matrix solver such as outer iteration based on conjugate residual. As a result coarse space representations of the operator remain nearest neighbour, giving an 8 point stencil rather than the 81 point stencil used in HDCG. It is hoped this may make it viable to recalculate the matrix elements of the little Dirac operator in an HMC evolution.

arXiv comment2 figures, 6 pages

References in corpus (6)

• Adaptive Multigrid Algorithm for Lattice QCD
• Hierarchically deflated conjugate gradient
• An adaptive aggregation based domain decomposition multilevel method for the lattice wilson dirac operator: multilevel results
• Adaptive Aggregation Based Domain Decomposition Multigrid for the Lattice Wilson Dirac Operator
• The role of multigrid algorithms for LQCD
• The removal of critical slowing down

Cited by in corpus (1)

• Optimizing Staggered Multigrid for Exascale performance