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Applied Numerical Algorithms Group

Peter Schwartz

Peter O. Schwartz
Research Scientist
Phone: +1 510 486 7507
Fax: +1 510 486 6900

My interests are in algorithms for the numerical solution to partial differential equations. In particular, I focus on cut-cell methods for complex geometry, issues related to interface tracking, and moving boundaries. I have most often applied these algorithms to two environmental fluid flow projects:,  a model of the the San Francisco Bay and Delta and a model to track the flow of the Anrtarctic ice sheet.

Journal Articles

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,

Schwartz, P., and Colella P., "A Second-Order Accurate Method for Solving the Signed Distance Function Equation", Communications in Applied Mathematics and Computational Science, Vol. 5 (2010), No. 1, 81-97, 2010,

Schwartz, P., Barad, M., Colella, P., Ligocki, T.J., "A Cartesian Grid Embedded Boundary Method for the Heat Equation and Poisson's Equation in Three Dimensions", Journal of Computational Physics. Vol. 211 (2006), pp. 531-550., 2006, LBNL 56607,

Schwartz, P., Adalsteinsson, D., Colella, P., Arkin, A.P., Onsum, M., "Numerical computation of diffusion on a surface", Proc. Nat. Acad. Sci. Vol. 102 (2005), pp. 11151-11156, 2005,

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

M. Dorf, M. Dorr, J. Hittinger, T. Rognlien, P. Colella, P. Schwartz,R. Cohen, W. Lee, "Modeling Edge Plasma with the Continuum Kinetic Code COGENT", 2015,

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,

T.J. Ligocki, P.O. Schwartz, J. Percelay, P. Colella, "Embedded Boundary Grid Generation using the Divergence Theorem, Implicit Functions, and Constructive Solid Geometry", 2008 J. Phys.: Conf. Ser. 125 012080, 2008,

Deschamps, T., Schwartz, P., Trebotich, D., Colella, P., Malladi, R., Saloner, D., "Vessel Segmentation and Blood Flow Simulation Using Level Sets and Embedded Boundary Methods", Elsevier International Congress Series, 1268, pp. 75-80. Presented at the 18th Conference and Exhibition for Computer Assisted Radiology and Surgery, June, 2004, 2004,


Daniel Martin, Peter O. Schwartz, Esmond G. Ng, Improving Grounding Line Discretization using an Embedded-Boundary Approach in BISICLES, 2015 SIAM Conference on Computational Science and Engineering, March 14, 2015,

R.H. Cohen,M Dorf, M. Dorr, D.D. Ryutov, P.Schwartz, Plans for Extending COGENT to Model Snowflake Divertors, APS-DPP Meeting, New Orleans LA, October 27, 2014,


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,

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,


D.F. Martin, H.S. Johansen, P.O. Schwartz, E.G. Ng, "Improved Discretization of Grounding Lines and Calving Fronts using an Embedded-Boundary Approach in BISICLES", European Geosciences Union General Assembly, April 10, 2019,

R.H. Cohen, M. Dorf, M. Dorr, D.D. Ryutov, P.Schwartz, "Plans for Extending COGENT to Model Snowflake Divertors", ESL Team Meeting, GA, September 30, 2014,