Largescale optimizationbased nonnegative computational framework for diffusion equations: Parallel implementation and performance studies
Abstract
It is wellknown that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving selfadjoint diffusion equations, does not meet maximum principles and the nonnegative constraint for anisotropic diffusion equations. Recently, optimizationbased methodologies that satisfy maximum principles and the nonnegative constraint for steadystate and transient diffusiontype equations have been proposed. To date, these methodologies have been tested only on smallscale academic problems. The purpose of this paper is to systematically study the performance of the nonnegative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, used for the parallel environment and optimization solvers. For largescale 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 stateoftheart HPC systems, and a singlecore performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed nonnegative computational framework for diffusiontype equations exhibits excellent strong scaling for realworld largescale 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 Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1296665
 Report Number(s):
 LAUR1524900
Journal ID: ISSN 08857474
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Scientific Computing
 Additional Journal Information:
 Journal Name: Journal of Scientific Computing; Journal ID: ISSN 08857474
 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. Largescale optimizationbased nonnegative computational framework for diffusion equations: Parallel implementation and performance studies. United States: N. p., 2016.
Web. doi:10.1007/s1091501602505.
Chang, Justin, Karra, Satish, & Nakshatrala, Kalyana B. Largescale optimizationbased nonnegative computational framework for diffusion equations: Parallel implementation and performance studies. United States. doi:10.1007/s1091501602505.
Chang, Justin, Karra, Satish, and Nakshatrala, Kalyana B. Tue .
"Largescale optimizationbased nonnegative computational framework for diffusion equations: Parallel implementation and performance studies". United States. doi:10.1007/s1091501602505. https://www.osti.gov/servlets/purl/1296665.
@article{osti_1296665,
title = {Largescale optimizationbased nonnegative computational framework for diffusion equations: Parallel implementation and performance studies},
author = {Chang, Justin and Karra, Satish and Nakshatrala, Kalyana B.},
abstractNote = {It is wellknown that the standard Galerkin formulation, which is often the formulation of choice under the finite element method for solving selfadjoint diffusion equations, does not meet maximum principles and the nonnegative constraint for anisotropic diffusion equations. Recently, optimizationbased methodologies that satisfy maximum principles and the nonnegative constraint for steadystate and transient diffusiontype equations have been proposed. To date, these methodologies have been tested only on smallscale academic problems. The purpose of this paper is to systematically study the performance of the nonnegative methodology in the context of high performance computing (HPC). PETSc and TAO libraries are, respectively, used for the parallel environment and optimization solvers. For largescale 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 stateoftheart HPC systems, and a singlecore performance model is used to better characterize the efficiency of the solvers. Furthermore, our studies indicate that the proposed nonnegative computational framework for diffusiontype equations exhibits excellent strong scaling for realworld largescale problems.},
doi = {10.1007/s1091501602505},
journal = {Journal of Scientific Computing},
number = ,
volume = ,
place = {United States},
year = {2016},
month = {7}
}
Web of Science