Research Affiliations
I am an affiliated faculty member in the Department of Scientific Computing at Florida State University.
Research Interests
My current research interests include numerical analysis,
numerical linear algebra, linear solvers,
multiscale modeling, and
domain decomposition methods.
A description of some current and past projects appears below.
Mesoscopic Material Modeling
I am the Sandia CoPI for the Collaboratory on Mathematics for Mesoscopic Modeling of Materials (CM4), led by
George Karniadakis (PNNL / Brown University). The Sandia research team includes Pavel Bochev,
Jonathan Hu, and Christopher Siefert.
This project focuses on developing rigorous mathematical foundations for understanding and controlling fundamental mechanisms in mesoscale processes to enable scalable synthesis of complex materials,
through the design of efficient modeling methods and corresponding scalable algorithms.
This large multiinstitution project is funded by the DOE Office of Advanced Scientific Computing Research (ASCR) as one of the
Mathematical Multifaceted Integrated Capabilities Centers (MMICCs). Drs. Sandy Landsberg and Steven Lee are the program managers.
Peridynamics
The peridynamic theory of continuum mechanics is a nonlocal extension of classical mechanics which allows direct interactions between points separated by a finite distance.
The maximum interaction distance between any two points defines a length scale, making peridynamics suitable for multiscale modeling. Peridynamics is based upon integral
equations, and was developed to allow discontinuous media (e.g., fracture and fragmentation). Peridynamics was first proposed by Stewart Silling.
Computational Peridynamics
Computational peridynamics is a special variety of of computational mechanics, and is an active area of research and development. Known optimal methods and algorithms for classical (local) computational mechanics frequently do not map
directly onto a nonlocal setting. I am interested in the development of algorithms and computational methods for nonlocal models.
A particular discretization of the peridynamic model has the same computational structure as
classical molecular dynamics. I am the principal author of the peridynamic model implemented within Sandia's
massively parallel molecular dynamics code, LAMMPS. This is the only opensource peridynamic code, and was developed jointly with Pablo Seleson
and Steve Plimpton. Visit my software page for more information.
I develop for the Sandia Peridynamic code, Peridigm.
Peridigm is a based upon an agile components methodology to enable massively parallel multiphysics peridynamic simulations. Peridigm provides for optimization, UQ, error estimation, and calibration through
an interface to Sandia's DAKOTA project.
This is joint work with Dave Littlewood, John Mitchell, and Stewart Silling.
Publications
—
Pablo Seleson and Michael L. Parks,
On the Role of the Influence Function in the Peridynamic Theory,
International Journal for Multiscale Computational Engineering,
To appear, 2010.
—
Michael L. Parks, Pablo Seleson, Steven J. Plimpton, Richard B. Lehoucq, and Stewart A. Silling,
Peridynamics with LAMMPS: A User Guide,
Technical Report SAND20105549, Sandia National Laboratories, August 2010.
—
Michael L. Parks, Richard B. Lehoucq, Steven J. Plimpton, and Stewart A. Silling,
Implementing Peridynamics within a Molecular Dynamics Code,
Computer Physics Communications, 179(11), pp. 777783, 2008.
Peridynamics as a Multiscale Model
Peridynamics is a nonlocal formulation of continuum mechanics.
The maximum interaction distance between any two points defines a length scale, making peridynamics suitable for multiscale modeling.
Much of my work has been in the development of peridynamics as a continualization of molecular dynamics.
Publications
—
Pablo Seleson, Michael L. Parks, Max Gunzburger, and Richard B. Lehoucq,
Peridynamics as an Upscaling of Molecular Dynamics,
Multiscale Modeling and Simulation, 8(1), pp. 204227, 2009.
Linear Solvers
My research in iterative methods focuses primarily on the development of robust solvers and preconditioners for illconditioned linear systems.
Scalable Solvers for FluidDFTs
Fluid density functional theories (FluidDFTs) enable modeling and simulation of a wide range of applications, including fluids at interfaces, colloidal fluids, wetting, porous media, and biological mechanisms at the cellular level.
FluidDFT problems result in a collection of highly nonlinear problems that usually require continuation algorithms around a fullycoupled Newton solver.
As most of the computation time is spent in the linear solver, and because problem scalability is ultimately determined by the scalability
of the linear solver, scalable preconditioned iterative solvers are a critical capability for FluidDFT problems and is the key to enabling realistic solutions for important problems.
I develop for Sandia's Tramonto FluidDFT code. My work is funded by ASCR, in collaboration with
David Day, Amalie Frischknecht, Mike Heroux and Laurie Frink.
Krylov Subspace Recycling
Many problems in engineering and physics require the solution of a large sequence of linear systems.
We can reduce the cost of solving subsequent systems in the sequence by recycling information from
previous systems. I develop a family of solvers based upon a technique known as "Krylov Subspace Recycling".
The Belos package in Trilinos currently contains a recycling GMRES solver (GCRODR) and a recycling CG solver (RCG). For some problems, the iteration count
required to solve a linear system can be cut by a factor of two.
For Matlab and Trilinos implementations of recycling solvers, please see my software page.
Publications
—
Michael L. Parks, Eric de Sturler, Greg Mackey, Duane Johnson, and Spandan Maiti,
Recycling Krylov Subspaces for Sequences of Linear Systems,
SIAM Journal on Scientific Computing, 28(5), pp. 16511674, 2006.
Multiscale Modeling
Multiscale modeling refers to the use of models capturing information at multiple spatial and temporal scales. Such models are particularly important when, for example, microscale phenomena dictate macroscale response.
Peridynamics as a Multiscale Model
The maximum interaction distance between any two points in a peridynamic model induces a length scale, making peridynamics suitable for multiscale modeling. See above for more.
AtomistictoContinuum Coupling
The deformation and failure of many engineering materials are inherently multiscale processes.
Models for such processes frequently call for decomposition of the material domain into atomistic and continuum
subdomains, where the continuum subdomain is modeled via a finite element analysis.
This coupling enables a continuum calculation to
be performed over the majority of a domain while limiting
the more expensive atomistic simulation to some small subset of the domain.
The treatment of the interface between these subdomains
is what distinguishes one atomistictocontinuum coupling method from another.
Along with Santiago Badia, Pavel Bochev,
Jacob Fish, Max Gunzburger,
Rich Lehoucq, and Mark Shephard,
I developed an atomistictocontinuumm coupling method called blending.
Recognizing atomistictocontinuum coupling as heterogeneous domain decomposition, it makes sense to apply conventional domain decomposition methods
to this problem. I developed a method for atomistictocontinuum coupling based upon alternating Schwartz.
With Greg Wagner, Reese Jones, and Jeremy Templeton I also developed a methodology for atomistictocontinuum thermal coupling. This was deployed in LAMMPS by Reese Jones, Jeremy Templeton, and Jon Zimmerman.
Publications
—
Pavel Bochev, Richard Lehoucq, Michael Parks, Santiago Badia, and Max Gunzburger,
Blending methods for coupling atomistic and continuum models,
in Multiscale Methods: Bridging the Scales in Science and Engineering,
ed. by Jacob Fish, Oxford University Press, pp. 165191, 2009.
—
Santiago Badia, Pavel B. Bochev, Max Gunzburger, Richard B. Lehoucq, Michael L. Parks,
Bridging Methods for Coupling Atomistic and Continuum Models, in LargeScale Scientific Computing 6th International
Conference, Sozopol, Bulgaria, June 59, 2007, I. Lirkov, S. Margenov, and J. Wasniewski, eds., vol.
4818 of Lecture Notes in Computer Science, pp. 1627, 2009.
—
Michael L. Parks, Pavel B. Bochev, and Richard B. Lehoucq,
Connecting AtomistictoContinuum Coupling and Domain Decomposition,
Multiscale Modeling and Simulation, 7, pp. 362380, 2008.
—
Santiago Badia, Michael L. Parks, Pavel B. Bochev, Max Gunzburger, and Richard B. Lehoucq,
On AtomistictoContinuum Coupling by Blending,
Multiscale Modeling and Simulation, 7, pp. 381406, 2008.
—
Santiago Badia, Pavel. B. Bochev, Jacob Fish, Max D. Gunzburger, Richard B. Lehoucq, Mohan. A. Nuggehally, Michael. L. Parks,
A ForceBased Blending Model for AtomistictoContinuum Coupling,
International Journal for Multiscale Computational Engineering,
5, pp. 387406, 2007.
—
Jacob Fish, Mohan A. Nuggehally, Mark S. Shephard, Catalin R. Picu, Santiago Badia, Michael L. Parks, and Max Gunzburger,
Concurrent AtC coupling based on a blend of the continuum stress and the atomistic force,
Computer Methods in Applied Mechanics and Engineering,
196, pp. 45484560, 2007.
—
Gregory J. Wagner, Reese E. Jones, Jeremy A. Templeton, and Michael L. Parks,
An AtomistictoContinuum Coupling Method for Heat Transfer in Solids,
Computer Methods in Applied Mechanics and Engineering, 197, pp. 33513365, 2008.
Domain Decomposition
Domain decomposition is the method of splitting a mathematical and computational problem into coupled problems on smaller subdomains that partition the original domain. This is a necessary process to map a
computational problem onto a parallel computer.
MeshTying
In the case where two domains sharing a common curved interface are meshed independently,
the domains will generally have an inconsistent description of that boundary. A minimal
requirement for any proposed mechanism to tie these two meshes together is that the resulting
finite element formulation pass a firstorder patch test, whether or not the two discretizations
of the shared boundary coincide. Along with Pavel Bochev and Louis Romero, I developed a
novel computationally efficient Lagrangemultiplier method for tying together independently
meshed subdomains with noncoincident contact boundaries in two dimensions.
Publications
— Michael L. Parks, Louis A. Romero, and Pavel B. Bochev,
A Novel LagrangeMultiplier Based Method for Consistent Mesh Tying,
Computer Methods in Applied Mechanics and Engineering,
196, pp. 33353347, 2007.
KKT Preconditioners for FETI Methods
Preconditioners for KKT (KarushKuhnTucker) linear systems have been studied extensively.
The onelevel finite element tearing and interconnecting (FETI) method produces
a linear system of this form. In the fourth chapter of my
Ph.D. dissertation,
I show new connections between
recently proposed KKT preconditioners and solvers and the onelevel FETI method. These
connections provide a new perspective on the analysis of FETI preconditioners by leveraging
work for KKT systems. In particular, they provide a means of bounding the eigenvalues
of preconditioned FETI systems, and thus the rate of convergence of an iterative solver.
This theoretical framework gives a means to analyze the usefulness of improvements to
FETI preconditioners.
Chromatography
Chromatography is a family of analytical chemistry techniques for the separation
of mixtures. In gas chromatography, a chemical sample separates into its constituent components
as it travels along a long thin column. In a traditional chromatograph, the column has a
circular cross section. With the advent of MEMS technology, columns can be miniaturized
to fit on a single chip. Unfortunately, these columns cannot be manufactured to have a
circular crosssection. With Louis Romero, Joshua Whiting, and Joe Simonson, I
analyzed the effects of noncircular crosssectional geometry on column performance.
Publications
— Michael L. Parks, Louis A. Romero, and Joshua Whiting,
A Reduced Order Model for the Study of Asymmetries in Linear Gas Chromatography for Homogeneous Tubular Columns,
Technical Report SAND20054868,
Sandia National Laboratories, August 2005.
— Michael L. Parks, Louis A. Romero, TaylorAris Dispersion in High Aspect Ratio Columns of Nearly Rectangular
CrossSection, Mathematical and Computer Modelling, 46, pp. 699717, 2007.
Previous Research
As a masters student in the Department of Computer Science at Virginia Tech, my work was interdisciplinary
between the physics and computer science departments.
—
Masters Thesis:
An Efficient Numeric Computation of a Phase Diagram in the Biased Diffusion of Two Species
(Advisor: Cal Ribbens) (2000)
As an undergraduate at Virginia Tech earning dual degrees in the departments of computer science and physics, I participated
in undergraduate research in both departments.
—
Undergraduate Thesis: The Construction and Analysis of Factorial Experiments: Application to
Tribochemical Vapor Deposition (1998)
—
Tribochemical Vapor Deposition  A New Deposition Technique: Poster at the 1997 Gordon Research
Conference on Solid State Studies in Ceramics (with
Jimmy Ritter) (1997)
—
Virginia Tech Physics Department: Tribochemical Vapor Deposition (TCVD) Experiment (199698)
—
Virginia Tech Computer Science Department:
Learning in Networked Communities Project on Collaborative Education (1996)
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Michael L. Parks
Contact
Email:
Michael L. Parks
(505)8450512 (Phone)
(505)8457442 (Fax)
Mailing address
Sandia National Laboratories
P.O. Box 5800, MS 1320 Albuquerque, NM 871851320
UPS, FedEx, etc.
Sandia National Laboratories
1515 Eubank Ave. Albuquerque, NM 87123
