Muralikrishnan, Sriramkrishnan | Engineering Papers

DOE OSTI2024

Scaling and performance portability of the particle-in-cell scheme for plasma physics applications through mini-apps targeting exascale architectures

We perform a scaling and performance portability study of the particle-in-cell scheme for plasma physics applications through a set of mini-apps we name "Alpine", which can make use of exascale computing capabilities. The mini-apps are based on Independent Parallel Particle Layer, a framework that is designed around performance portable and dimension independent particles and fields. We benchmark the simulations with varying parameters such as grid resolutions (5123 to 20483) and number of simulation particles (109 to 1011) with the following mini-apps: weak and strong Landau damping, bump-on-tail and two-stream instabilities, and the dynamics of an electron bunch in a charge-neutral Penning trap. We show strong and weak scaling and analyze the performance of different components on several pre-exascale architectures such as Piz-Daint, Cori, Summit and Perlmutter. While the scaling and portability study helps identify the performance critical components of the particle-in-cell scheme in the current state-of-the-art computing architectures, the mini-apps by themselves can be used to develop new algorithms and optimize their high performance implementations targeting exascale architectures.

Muralikrishnan, Sriramkrishnan↗

DOE OSTI2019

Unified Geometric Multigrid Algorithm for Hybridized High-Order Finite Element Methods

In this paper, we consider a standard elliptic partial differential equation and propose a geometric multigrid algorithm based on Dirichlet-to-Neumann (DtN) maps for hybridized high-order finite element methods. The proposed unified approach is applicable to any locally conservative hybridized finite element method including multinumerics with different hybridized methods in different parts of the domain. For these methods, the linear system involves only the unknowns residing on the mesh skeleton, and constructing intergrid transfer operators is therefore not trivial. The key to our geometric multigrid algorithm is the physics-based energy-preserving intergrid transfer operators which depend only on the fine scale DtN maps. Thanks to these operators, we completely avoid upscaling of parameters and no information regarding subgrid physics is explicitly required on coarse meshes. Moreover, our algorithm is agglomeration-based and can straightforwardly handle unstructured meshes. We perform extensive numerical studies with hybridized mixed methods, hybridized discontinuous Galerkin methods, weak Galerkin methods, and hybridized versions of interior penalty discontinuous Galerkin methods on a range of elliptic problems including subsurface flow through highly heterogeneous porous media. We compare the performance of different smoothers and analyze the effect of stabilization parameters on the scalability of the multigrid algorithm.

97 MATHEMATICS AND COMPUTING↗