Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies

Journal Article · Tue Jul 26 04:00:00 UTC 2016 · Journal of Scientific Computing

DOI: https://doi.org/10.1007/s10915-016-0250-5 · OSTI ID:1296665

Chang, Justin ^[1]; Karra, Satish ^[2]; Nakshatrala, Kalyana B. ^[1]

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1. Univ. of Houston, Houston, TX (United States)
2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

It is well-known that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving self-adjoint diffusion equations, does not meet maximum principles and the non-negative constraint for anisotropic diffusion equations. Recently, optimization-based methodologies that satisfy maximum principles and the non-negative constraint for steady-state and transient diffusion-type equations have been proposed. To date, these methodologies have been tested only on small-scale academic problems. The purpose of this paper is to systematically study the performance of the non-negative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, used for the parallel environment and optimization solvers. For large-scale problems, it is important for computational scientists to understand the computational performance of current algorithms available in these scientific libraries. The numerical experiments are conducted on the state-of-the-art HPC systems, and a single-core performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.

• Research Organization: Los Alamos National Laboratory (LANL)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC52-06NA25396
• OSTI ID: 1296665
• Report Number(s): LA-UR-15-24900
• Journal Information: Journal of Scientific Computing, Journal Name: Journal of Scientific Computing; ISSN 0885-7474
• Publisher: SpringerCopyright Statement
• Country of Publication: United States
• Language: English