Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies
Abstract
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.
- Authors:
-
- Univ. of Houston, Houston, TX (United States)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1296665
- Report Number(s):
- LA-UR-15-24900
Journal ID: ISSN 0885-7474
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Scientific Computing
- Additional Journal Information:
- Journal Name: Journal of Scientific Computing; Journal ID: ISSN 0885-7474
- Publisher:
- Springer
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Computer Science; Environmental Protection
Citation Formats
Chang, Justin, Karra, Satish, and Nakshatrala, Kalyana B. Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies. United States: N. p., 2016.
Web. doi:10.1007/s10915-016-0250-5.
Chang, Justin, Karra, Satish, & Nakshatrala, Kalyana B. Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies. United States. https://doi.org/10.1007/s10915-016-0250-5
Chang, Justin, Karra, Satish, and Nakshatrala, Kalyana B. Tue .
"Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies". United States. https://doi.org/10.1007/s10915-016-0250-5. https://www.osti.gov/servlets/purl/1296665.
@article{osti_1296665,
title = {Large-scale optimization-based non-negative computational framework for diffusion equations: Parallel implementation and performance studies},
author = {Chang, Justin and Karra, Satish and Nakshatrala, Kalyana B.},
abstractNote = {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.},
doi = {10.1007/s10915-016-0250-5},
journal = {Journal of Scientific Computing},
number = ,
volume = ,
place = {United States},
year = {Tue Jul 26 00:00:00 EDT 2016},
month = {Tue Jul 26 00:00:00 EDT 2016}
}
Web of Science
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