Optimization of Finite-Differencing Kernels for Numerical Relativity Applications

Abstract

A simple optimization strategy for the computation of 3D finite-differencing kernels on many-cores architectures is proposed. The 3D finite-differencing computation is split direction-by-direction and exploits two level of parallelism: in-core vectorization and multi-threads shared-memory parallelization. The main application of this method is to accelerate the high-order stencil computations in numerical relativity codes. Our proposed method provides substantial speedup in computations involving tensor contractions and 3D stencil calculations on different processor microarchitectures, including Intel Knight Landing.

GRAthena++: puncture evolutions on vertex-centered oct-tree AMR

“…Generic spatial field derivatives in the bulk (away from ∂Ω) are computed with high-order, centered, finite difference (FD) stencils whereas shift advection terms use stencils lopsided by one grid point Zlochower et al (2005); Husa et al (2008);Brügmann et al (2008); Chirvasa & Husa (2010). The implementation is based on Alfieri et al (2018) and utilizes C++ templates to offer flexibility in problem-specific accuracy demands without performance penalties. A similar approach is taken for implementation of the R and P operators discussed in §2.2.3.…”

“…These attractive properties served as a strong motivation in development of GR-Athena++ where we have implemented the Z4c formulation Bernuzzi & Hilditch (2010); Ruiz et al (2011); Weyhausen et al (2012); Hilditch et al (2013) of NR utilizing the (moving) puncture gauge Brandt & Brügmann (1997); Baker et al (2007); Campanelli et al (2006). We provide accurate and efficient extensions to derivative approximants through (templated) arbitrary-order FD based on Alfieri et al (2018). Our introduction of vertex-centered (VC) variable treatment (extending core cell-and facecentered functionality) is motivated by a desire to match any selected FD order in calculations that involve AMR.…”

Multithreaded Acceleration of 3D Mathematical Model for Ore Sintering

“…The article [16] is devoted to a method of multithreading optimization using OpenMP applied for two problems: wave equation and linearized Einstein equations. The presented pictures show good speedup scaling.…”