A massively parallel semi-Lagrangian algorithm for solving the transport equation
Abstract
The scalar transport equation underpins many models employed in science, engineering, technology and business. Application areas include, but are not restricted to, pollution transport, weather forecasting, video analysis and encoding (the optical flow equation), options and stock pricing (the Black-Scholes equation) and spatially explicit ecological models. Unfortunately finding numerical solutions to this equation which are fast and accurate is not trivial. Moreover, finding such numerical algorithms that can be implemented on high performance computer architectures efficiently is challenging. In this paper the authors describe a massively parallel algorithm for solving the advection portion of the transport equation. We present an approach here which is different to that used in most transport models and which we have tried and tested for various scenarios. The approach employs an intelligent domain decomposition based on the vector field of the system equations and thus automatically partitions the computational domain into algorithmically autonomous regions. The solution of a classic pure advection transport problem is shown to be conservative, monotonic and highly accurate at large time steps. Additionally we demonstrate that the algorithm is highly efficient for high performance computer architectures and thus offers a route towards massively parallel application.
- Authors:
-
- Richard Stockton College of New Jersey
- ORNL
- Publication Date:
- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Org.:
- USDOE Laboratory Directed Research and Development (LDRD) Program
- OSTI Identifier:
- 990228
- DOE Contract Number:
- DE-AC05-00OR22725
- Resource Type:
- Conference
- Resource Relation:
- Conference: Internation Conference on Computational Sciences 2010: "Celebrating 10 years of Advancing Computational Thinking", Amsterdam, Netherlands, 20100531, 20100602
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 54 ENVIRONMENTAL SCIENCES; ADVECTION; ALGORITHMS; BUSINESS; COMPUTER ARCHITECTURE; FORECASTING; NUMERICAL SOLUTION; PERFORMANCE; POLLUTION; SCALARS; TRANSPORT; VECTOR FIELDS; WEATHER; parallel computing; semi-lagrangian; transport equation; numerical algorithm
Citation Formats
Manson, Russell, and Wang, Dali. A massively parallel semi-Lagrangian algorithm for solving the transport equation. United States: N. p., 2010.
Web.
Manson, Russell, & Wang, Dali. A massively parallel semi-Lagrangian algorithm for solving the transport equation. United States.
Manson, Russell, and Wang, Dali. 2010.
"A massively parallel semi-Lagrangian algorithm for solving the transport equation". United States.
@article{osti_990228,
title = {A massively parallel semi-Lagrangian algorithm for solving the transport equation},
author = {Manson, Russell and Wang, Dali},
abstractNote = {The scalar transport equation underpins many models employed in science, engineering, technology and business. Application areas include, but are not restricted to, pollution transport, weather forecasting, video analysis and encoding (the optical flow equation), options and stock pricing (the Black-Scholes equation) and spatially explicit ecological models. Unfortunately finding numerical solutions to this equation which are fast and accurate is not trivial. Moreover, finding such numerical algorithms that can be implemented on high performance computer architectures efficiently is challenging. In this paper the authors describe a massively parallel algorithm for solving the advection portion of the transport equation. We present an approach here which is different to that used in most transport models and which we have tried and tested for various scenarios. The approach employs an intelligent domain decomposition based on the vector field of the system equations and thus automatically partitions the computational domain into algorithmically autonomous regions. The solution of a classic pure advection transport problem is shown to be conservative, monotonic and highly accurate at large time steps. Additionally we demonstrate that the algorithm is highly efficient for high performance computer architectures and thus offers a route towards massively parallel application.},
doi = {},
url = {https://www.osti.gov/biblio/990228},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Fri Jan 01 00:00:00 EST 2010},
month = {Fri Jan 01 00:00:00 EST 2010}
}