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Title: 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:
 [1];  [2];  [1]
  1. Univ. of Houston, Houston, TX (United States)
  2. 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):
LA-UR-15-24900
Journal ID: ISSN 0885-7474
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Journal Article: 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. doi: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. doi: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}
}

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