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Applied Numerical Algorithms Group

Daniel T. Graves

Dan Graves
Computer Systems Engineer
Phone: +1 510 486 8697
Fax: +1 510 486 6900

Dr. Daniel Graves received his BS from the University  of New Hampshire in 1989.  He received his Ph.D. from the University of California, Berkeley in 1996.  Both degrees were in Mechanical Engineering.  He has worked at Lawrence Berkeley National Laboratory since 1997.  He is a senior member of the Applied Numerical Algorithms Group.

His research is in the area of numerical methods for partial differential equations, with contributions in the areas of adaptive mesh refinement, Cartesian grid embedded boundary methods, massively parallel computation and library design for scientific computing.  He has contributed significantly in algorithms for incompressible flow, shock physics, viscoelastic flows and elliptic solvers for magneto-hydrodynamics.

Journal Articles

Weiqun Zhang, Ann Almgren, Vince Beckner, John Bell, Johannes Blashke, Cy Chan, Marcus Day, Brian Friesen, Kevin Gott, Daniel Graves, Max P. Katz, Andrew Myers, Tan Nguyen, Andrew Nonaka, Michele Rosso, Samuel Williams, Michael Zingale, "AMReX: a framework for block-structured adaptive mesh refinement", Journal of Open Source Software, May 2019, doi: 10.21105/joss.01370

Dharshi Devendran, Daniel T. Graves, Hans Johansen,Terry Ligocki, "A Fourth Order Cartesian Grid Embedded Boundary Method for Poisson's Equation", Communications in Applied Mathematics and Computational Science, edited by Silvio Levy, May 12, 2017, 12:51-79, doi: DOI 10.2140/camcos.2017.12.51

D. Devendran, D. T. Graves, H. Johansen, "A higher-order finite-volume discretization method for Poisson's equation in cut cell geometries", submitted to SIAM Journal on Scientific Computing (preprint on arxiv), 2015,

Peter Schwartz, Julie Percelay, Terry J. Ligocki, Hans Johansen, Daniel T. Graves, Dharshi Devendran, Phillip Colella, Eli Ateljevich, "High-accuracy embedded boundary grid generation using the divergence theorem", Communications in Applied Mathematics and Computational Science 10-1 (2015), 83--96. DOI 10.2140/camcos.2015.10.83, March 31, 2015,

Anshu Dubey, Ann Almgren, John Bell, Martin Berzins, Steve Brandt, Greg Bryan, Phillip Colella, Daniel Graves, Michael Lijewski, Frank L\ offler, others, "A survey of high level frameworks in block-structured adaptive mesh refinement packages", Journal of Parallel and Distributed Computing, 2014, 74:3217--3227, doi: 10.1016/j.jpdc.2014.07.001

Daniel T. Graves, Phillip Colella, David Modiano, Jeffrey Johnson, Bjorn Sjogreen, Xinfeng Gao, "A Cartesian Grid Embedded Boundary Method for the Compressible Navier Stokes Equations", Communications in Applied Mathematics and Computational Science, December 23, 2013,

In this paper, we present an unsplit method for the time-dependent
  compressible Navier-Stokes equations in two and three dimensions.
  We use a a conservative, second-order Godunov algorithm.
  We use a Cartesian grid, embedded boundary method to resolve complex
  boundaries.  We solve for viscous and conductive terms with a
  second-order semi-implicit algorithm.  We demonstrate second-order
  accuracy in solutions of smooth problems in smooth geometries and
  demonstrate robust behavior for strongly discontinuous initial
  conditions in complex geometries.

S.L. Cornford, D.F. Martin, D.T. Graves, D.F. Ranken, A.M. Le Brocq, R.M. Gladstone, A.J. Payne, E.G. Ng, W.H. Lipscomb, "Adaptive mesh, finite volume modeling of marine ice sheets", Journal of Computational Physics, 232(1):529-549, 2013,

R.K. Crockett, P. Colella, and D.T. Graves, "A Cartesian Grid Embedded Boundary Method for Solving the Poisson and Heat Equations with Discontinuous Coefficients in Three Dimensions", Journal of Computational Physics , 230(7):2451-2469, 2010,

A. Nonaka, D. Trebotich, G. H. Miller, D. T. Graves, and P. Colella, "A Higher-Order Upwind Method for Viscoelastic Flow", Comm. App. Math. and Comp. Sci., 4(1):57-83, 2009,

D. T. Graves, D Trebotich, G. H. Miller, P. Colella, "An Efficient Solver for the Equations of Resistive MHD with Spatially-Varying Resistivity", Journal of Computational Physics Vol 227 (2008) pp.4797-4804., 2008,

Martin, D.F., Colella, P., and Graves, D.T., "A Cell-Centered Adaptive Projection Method for the Incompressible Navier-Stokes Equations in Three Dimensions", Journal of Computational Physics Vol 227 (2008) pp. 1863-1886., 2008, LBNL 62025, doi: 10.1016/

Colella, P., Graves, D.T., Keen, B.J., Modiano, D., "A Cartesian Grid Embedded Boundary Method for Hyperbolic Conservation Laws", Journal of Computational Physics. Vol. 211 (2006), pp. 347-366., 2006, LBNL 56420,

Trebotich, D., Miller, G.H., Colella, P., Graves, D.T., Martin, D.F., Schwartz, P.O., "A Tightly Coupled Particle-Fluid Model for DNA-Laden Flows in Complex Microscale Geometries", Computational Fluid and Solid Mechanics 2005, pp. 1018-1022, Elsevier (K. J. Bathe editor), 2005,

Conference Papers

Anshu Dubey, Hajime Fujita, Daniel T. Graves, Andrew Chien Devesh Tiwari, "Granularity and the Cost of Error Recovery in Resilient AMR Scientific Applications", SuperComputing 2016, August 10, 2016,

Anshu Dubey, Daniel T. Graves, "A Design Proposal for a Next Generation Scientific Software Framework", EuroPar 2015, July 31, 2015,

Gunther H. Weber, Hans Johansen, Daniel T. Graves, Terry J. Ligocki, "Simulating Urban Environments for Energy Analysis", Proceedings Visualization in Environmental Sciences (EnvirVis), 2014, LBNL 6652E,

Chaopeng Shen, David Trebotich, Sergi Molins, Daniel T Graves, BV Straalen, DT Graves, T Ligocki, CI Steefel, "High performance computations of subsurface reactive transport processes at the pore scale", Proceedings of SciDAC, 2011,

B. Van Straalen, P. Colella, D. T. Graves, N. Keen, "Petascale Block-Structured AMR Applications Without Distributed Meta-data", Euro-Par 2011 Parallel Processing - 17th International Conference, Euro-Par 2011, August 29 - September 2, 2011, Proceedings, Part II. Lecture Notes in Computer Science 6853 Springer 2011, ISBN 978-3-642-23396-8, Bordeaux, France, 2011,

E. Ateljevich, P. Colella, D.T. Graves, T.J. Ligocki, J. Percelay, P.O. Schwartz, Q. Shu, "CFD Modeling in the San Francisco Bay and Delta", 2009 Proceedings of the Fourth SIAM Conference on Mathematics for Industry (MI09), pp. 99-107, 2010,

D. Trebotich, B.V. Straalen, D. Graves and P. Colella, "Performance of Embedded Boundary Methods for CFD with Complex Geometry", 2008 J. Phys.: Conf. Ser. 125 012083, 2008,

P. Colella, D. Graves, T. Ligocki, D. Trebotich and B.V. Straalen, "Embedded Boundary Algorithms and Software for Partial Differential Equations", 2008 J. Phys.: Conf. Ser. 125 012084, 2008,

Colella, P., Graves, D.T., Modiano, D., Puckett, E.G., Sussman, M., "An Embedded Boundary / Volume of Fluid Method for Free Surface Flows in Irregular Geometries", ASME Paper FEDSM99-7108, in Proceedings of the 3rd ASME/JSME Joint Fluids Engineering Conference, 18-23 July, San Francisco, CA, 1999,

Book Chapters

B. Van Straalen, D. Trebotich, A. Ovsyannikov and D.T. Graves, "Scalable Structured Adaptive Mesh Refinement with Complex Geometry", Exascale Scientific Applications: Programming Approaches for Scalability, Performance, and Portability, edited by Straatsma, T., Antypas, K., Williams, T., (Chapman and Hall/CRC: November 9, 2017)


P. Colella, D. T. Graves, T. J. Ligocki, G.H. Miller , D. Modiano, P.O. Schwartz, B. Van Straalen, J. Pillod, D. Trebotich, M. Barad, "EBChombo Software Package for Cartesian Grid, Embedded Boundary Applications", Lawrence Berkeley National Laboratory Technical Report LBNL-6615E, January 9, 2015,

M. Adams, P. Colella, D. T. Graves, J.N. Johnson, N.D. Keen, T. J. Ligocki. D. F. Martin. P.W. McCorquodale, D. Modiano. P.O. Schwartz, T.D. Sternberg, B. Van Straalen, "Chombo Software Package for AMR Applications - Design Document", Lawrence Berkeley National Laboratory Technical Report LBNL-6616E, January 9, 2015,

Dharshi Devendran, Daniel T. Graves, Hans Johansen, "A Hybrid Multigrid Algorithm for Poisson's equation using an Adaptive, Fourth Order Treatment of Cut Cells", LBNL Report Number: LBNL-1004329, November 11, 2014,

Brian Van Straalen, David Trebotich, Terry Ligocki, Daniel T. Graves, Phillip Colella, Michael Barad, "An Adaptive Cartesian Grid Embedded Boundary Method for the Incompressible Navier Stokes Equations in Complex Geometry", LBNL Report Number: LBNL-1003767, 2012, LBNL LBNL Report Numb,

We present a second-order accurate projection method to solve the
  incompressible Navier-Stokes equations on irregular domains in two
  and three dimensions.  We use a finite-volume discretization
  obtained from intersecting the irregular domain boundary with a
  Cartesian grid.  We address the small-cell stability problem
  associated with such methods by hybridizing a conservative
  discretization of the advective terms with a stable, nonconservative
  discretization at irregular control volumes, and redistributing the
  difference to nearby cells.  Our projection is based upon a
  finite-volume discretization of Poisson's equation.  We use a
  second-order, $L^\infty$-stable algorithm to advance in time.  Block
  structured local refinement is applied in space.  The resulting
  method is second-order accurate in $L^1$ for smooth problems.  We
  demonstrate the method on benchmark problems for flow past a
  cylinder in 2D and a sphere in 3D as well as flows in 3D geometries
  obtained from image data.

Colella, P., Graves, D.T., Greenough, J.A., "A Second-Order Method for Interface Recontruction in Orthogonal Coordinate Systems", January 2002, LBNL 45244,


An Approximate Projection Method Suitable for the Modeling of Rapidly Rotating Flows, Graves, D.T., 1996,