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MATH 4820

GSMM Camps:

GSMMC 2017
GSMMC 2016
GSMMC 2015
GSMMC 2014
GSMMC 2013

MPI Workshops:

MPI 2017 (NJIT)
MPI 2016 (Duke)
MPI 2015 (UD)
MPI 2014 (NJIT)
MPI 2013 (WPI)
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Mathematical Sciences
Donald Schwendeman

Professor and Department Head
Ph.D. California Institute of Technology
Computational and Applied Mathematics


Research

  • Interests:

    • Numerical methods for partial differential equations.
    • Fluid-structure interaction problems.
    • Electrodynamics and nanophontonics.
    • Gas dynamics and wave propagation.
    • Multiscale and multiphase reactive flow.
    • Adaptive mesh refinement and parallel algorithms.
    • Mathematical modeling and computations in industrial applications.

  • Collaborators:

    • Ash Kapila, Rensselaer Polytechnic Institute.
    • Bill Henshaw, Rensselaer Polytechnic Institute.
    • Jeff Banks, Rensselaer Polytechnic Institute.
    • Mark Short, Los Alamos National Laboratory.

  • Software:

    • Most of the algorithms and research results described in the publications below are available in Overture. The software is freely available at overtureframework.org

  • Recent publications (full list with links):

    • J. Gambino, A.K. Kapila and D.W. Schwendeman, Numerical study of multiscale compaction-initiated detonation, Shock Waves, 29 (2019), 1193-219.

    • J.B. Angel, J.W. Banks, W.D. Henshaw, M.J. Jenkinson, A.V. Kildishev, G. Kovacic, L. Prokopeva and D.W. Schwendeman, High-order Accurate Scheme for Maxwell's Equations with a Generalized Dispersive Material Model, J. Comput. Physics, 378 (2019), 411-444.

    • J.W. Banks, W.D. Henshaw, D.W. Schwendeman and Qi Tang, A stable partitioned FSI algorithm for rigid bodies and incompressible flow in three dimensions, J. Comput. Physics, 373 (2018), 455-492.

    • J.W. Banks, W.D. Henshaw, D.W. Schwendeman and Qi Tang, A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model Problem Analysis, J. Comput. Physics, 343 (2017), 432-468.

    • J.W. Banks, W.D. Henshaw, D.W. Schwendeman and Qi Tang, A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part II: General Formulation, J. Comput. Physics, 343 (2017), 469-500.

    • F. Meng, J.W. Banks, W.D. Henshaw and D.W. Schwendeman, CHAMP: A Stable and Accurate Partitioned Algorithm for Conjugate Heat Transfer, J. Comput. Physics, 344 (2017), 51-85.

    • J. Gambino, A.K. Kapila and D.W. Schwendeman, Sensitivity of run-to-detonation distance in practical explosives, Combust. Theory and Modeling, 20 (2016), 1088-1117.

    • L. Li, W.D. Henshaw, J.W. Banks, D.W. Schwendeman and G.A. Main, A stable partitioned FSI algorithm for incompressible flow and deforming beams, J. Comput. Physics, 312 (2016), 272-306.

    • J.W. Banks, W.D. Henshaw, A.K. Kapila and D.W. Schwendeman, An added-mass partition algorithm for fluid-structure interactions of compressible fluids and nonlinear solids, J. Comput. Physics, 305 (2016), 1037-1064.

    • A.K. Kapila, D.W. Schwendeman, J. Gambino, and W.D. Henshaw, A Numerical Study of the Dynamics of Detonation Initiated by Cavity Collapse, Shock Waves, 25 (2015), 545-572

    • D.W. Schwendeman, C.P. Please, B.S. Tilley and F. Hendriks, A homogenization analysis of the compressible flow between a slider and a moving rough surface, IMA J. Appl. Math., 80 (2015), 177-211.

    • J.W. Banks, W.D. Henshaw and D.W. Schwendeman, An analysis of a new stable partitioned algorithm for FSI problems. Part I: Incompressible flow and elastic solids, J. Comput. Physics, 269 (2014), 108-137.

    • J.W. Banks, W.D. Henshaw and D.W. Schwendeman, An analysis of a new stable partitioned algorithm for FSI problems. Part II. Incompressible flow and structural shells, J. Comput. Physics, 268 (2014), 399-416.


Course Information

  • Spring semester, 2020
    • Math 4820 Introduction to Numerical Methods for Differential Equations

  • Fall semester, 2019
    • Math 6890 Numerical Methods for Fluid Dynamics

  • Spring semester, 2019

  • Spring semester, 2018
    • Math 2400 Introduction to Differential Equations


Modeling Camps and Industry Workshops

  • Overview of the GSMM Camp and MPI Workshop

  • Graduate Student Mathematical Modeling (GSMM) Camps

    • GSMMC 2016, June 7-10, 2016 at Rensselaer Polytechnic Institute.
    • GSMMC 2015, June 16-19, 2015 at Rensselaer Polytechnic Institute.
    • GSMMC 2014, June 17-20, 2014 at Rensselaer Polytechnic Institute.
    • GSMMC 2013, June 11-14, 2013 at Rensselaer Polytechnic Institute.
    • GSMMC 2012, June 5-8, 2012 at Rensselaer Polytechnic Institute.
    • GSMMC 2011, June 11-12, 2011 at New Jersey Institute of Technology.
    • GSMMC 2010, June 8-11, 2010 at Rensselaer Polytechnic Institute.
    • GSMMC 2009, June 9-12, 2009 at Rensselaer Polytechnic Institute.
    • GSMMC 2008, June 10-13, 2008 at Rensselaer Polytechnic Institute.
    • GSMMC 2007, June 5-8, 2007 at Rensselaer Polytechnic Institute.
    • GSMMC 2006, June 6-9, 2006 at Rensselaer Polytechnic Institute.
    • GSMMC 2005, June 7-10, 2005 at Rensselaer Polytechnic Institute.
    • GSMMC 2004, June 15-18, 2004 at Rensselaer Polytechnic Institute.

  • Mathematical Problems in Industry (MPI) Workshops

    • MPI 2016, June 13-17, 2016 at Duke University.
    • MPI 2015, June 22-26, 2015 at the University of Delaware.
    • MPI 2014, June 23-27, 2014 at New Jersey Institute of Technology.
    • MPI 2013, June 17-21, 2013 at Worcester Polytechnic Institute.
    • MPI 2012, June 11-15, 2012 at the University of Delaware.
    • MPI 2011, June 13-17, 2011 at New Jersey Institute of Technology.
    • MPI 2010, June 14-18, 2010 at Rensselaer Polytechnic Institute.
    • MPI 2009, June 15-19, 2009 at the University of Delaware.
    • MPI 2008, June 16-20, 2008 at Worcester Polytechnic Institute.
    • MPI 2007, June 11-15, 2007 at the University of Delaware.
    • MPI 2006, June 12-16, 2006 at Olin College.
    • MPI 2005, June 13-17, 2005 at Worcester Polytechnic Institute.
    • MPI 2004, June 21-25, 2004 at the University of Delaware.
    • MPI 2003, June 2-6, 2003 at Worcester Polytechnic Institute.
    • MPI 2002, June 3-7, 2002 at Rensselaer Polytechnic Institute.
    • MPI 2001, June 4-8, 2001 at Rensselaer Polytechnic Institute.


Contact Information

Donald Schwendeman
Department of Mathematical Sciences
Rensselaer Polytechnic Institute
110 8th Street
Troy, New York 12180

Phone: (518) 276-2647
Fax: (518) 276-4824
Email: schwed@rpi.edu

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