TY - JOUR
T1 - Application of Jacobian-free Newton-Krylov with physics-based preconditioning to biogeochemical transport
AU - Hammond, G. E.
AU - Valocchi, A. J.
AU - Lichtner, P. C.
N1 - Funding Information:
This research was funded through the Department of Energy Computational Science Graduate Fellowship with supercomputing facilities provided by Los Alamos National Laboratory. We thank Dr. Vince Mousseau and Dr. Dana Knoll at Los Alamos National Laboratory for helpful discussions on the implementation of the Jacobian-free Newton–Krylov algorithm. We also thank Rachel Brennan, Professor Rob Sanford and Professor Charlie Werth at the University of Illinois at Urbana-Champaign for their input on modeling HERTZ.
PY - 2005/4
Y1 - 2005/4
N2 - Modern multicomponent geochemical transport models require the use of parallel computation for carrying out three-dimensional, field-scale simulations due to extreme memory and processing demands. However, to fully exploit the advanced computational power provided by today's supercomputers, innovative parallel algorithms are needed. We demonstrate the use of Jacobian-free Newton-Krylov (JFNK) within the Newton-Raphson method to reduce memory and processing requirements on high-performance computers. We also demonstrate the use of physics-based preconditioners, which are often necessary when using JFNK since no explicit Jacobian matrix is ever formed. We apply JFNK to simulate enhanced in situ bioremediation of a NAPL source zone, which entails highly coupled geochemical and biodegradation reactions. The algorithm's performance is evaluated and compared with conventional solvers and preconditioners. We found that JFNK provided substantial saving in memory (i.e. 30-60%) on problems utilizing up to 512 processors on LANL's ASCI Q. However, the performance based on wallclock time was less advantageous, coming out on par with conventional techniques. In addition, we illustrate deficiencies in physics-based preconditioner performance for biogeochemical transport problems with components that undergo significant sorption or form a local quasi-stationary state.
AB - Modern multicomponent geochemical transport models require the use of parallel computation for carrying out three-dimensional, field-scale simulations due to extreme memory and processing demands. However, to fully exploit the advanced computational power provided by today's supercomputers, innovative parallel algorithms are needed. We demonstrate the use of Jacobian-free Newton-Krylov (JFNK) within the Newton-Raphson method to reduce memory and processing requirements on high-performance computers. We also demonstrate the use of physics-based preconditioners, which are often necessary when using JFNK since no explicit Jacobian matrix is ever formed. We apply JFNK to simulate enhanced in situ bioremediation of a NAPL source zone, which entails highly coupled geochemical and biodegradation reactions. The algorithm's performance is evaluated and compared with conventional solvers and preconditioners. We found that JFNK provided substantial saving in memory (i.e. 30-60%) on problems utilizing up to 512 processors on LANL's ASCI Q. However, the performance based on wallclock time was less advantageous, coming out on par with conventional techniques. In addition, we illustrate deficiencies in physics-based preconditioner performance for biogeochemical transport problems with components that undergo significant sorption or form a local quasi-stationary state.
KW - Biogeochemical transport modeling
KW - Jacobian-free Newton-Krylov
KW - Modeling reductive dechlorination
KW - Physics-based preconditioning
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U2 - 10.1016/j.advwatres.2004.12.001
DO - 10.1016/j.advwatres.2004.12.001
M3 - Article
AN - SCOPUS:14644410459
SN - 0309-1708
VL - 28
SP - 359
EP - 376
JO - Advances in Water Resources
JF - Advances in Water Resources
IS - 4
ER -