Large-Scale Optimization-Based Non-negative Computational Framework for Diffusion Equations: Parallel Implementation and Performance Studies

作者：Chang J; Karra S; Nakshatrala K B^*

来源：Journal of Scientific Computing, 2017, 70(1): 243-271.

DOI：10.1007/s10915-016-0250-5

• High performance computing
• Anisotropic diffusion
• Maximum principles
• Non-negative constraint
• Large-scale optimization

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. Our studies indicate that the proposed non-negative computational framework for diffusion-type equations exhibits excellent strong scaling for real-world large-scale problems.
This figure shows the fate of chromium after 180 days using the single-field Galerkin formulation. The white regions indicate the violation of the non-negative constraint.
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• 出版日期2017-1
• 单位Los Alamos