Hierarchically deflated conjugate residual

Understand

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.