Professor, Department Head and Director, Center for Modeling, Optimization and Computational Analysis (MOCA)

Mathematical Sciences

(518) 276-2647

Dr. Schwendeman received his B.S.E. in Aerospace Engineering from the University of Michigan, and earned his Ph.D. in Applied Mathematics at the California Institute of Technology (Caltech) under the supervision of Professor G.B. Whitham, FRS. Dr. Schwendeman took a one-year postdoctoral research position at Caltech working with Professor H.B. Keller, before joining the faculty in the Department of Mathematical Sciences at Rensselaer as an assistant professor in August, 1987. Dr. Schwendeman received promotions to associate professor with tenure and then professor, and was named the Head of the Department of Mathematical Sciences in 2012.
Dr. Schwendeman's research focuses on the development and analysis of numerical methods for systems of partial differential equations (PDEs) that arise in applications of science and engineering. A significant portion of his work has centered around the development of numerical methods for systems of PDEs modeling wave phenomena in reactive and nonreactive flows. This work has included numerical studies of shock wave focusing and convergence, transonic and hypersonic aerodynamics, and multi-phase and multi-material high-speed reactive flow. In recent work, Dr. Schwendeman has developed a class of new numerical methods for fluid-structure interaction problems. All of this work has been in collaboration with researchers at national labs (Los Alamos and Lawrence Livermore) and at Rensselaer.
Dr. Schwendeman is also actively involved in undergraduate and graduate education and career development. He is a leader among the consortium of universities organizing the Mathematical Problems in Industry Workshop (1993-present), and the originator and lead organizer of the Graduate Student Mathematical Modeling Camp (2004-present). Dr. Schwendeman is also an active member of the NSF-funded Research Training Grant (RTG) program in the department, which supports the research and education of several graduate students and postdoctoral research fellows.

## Education

B.S.E., Aerospace Engineering, University of Michigan, 1981

Ph.D., Applied Mathematics, California Institute of Technology, 1986

## Focus Area

Numerical methods for PDEs, Fluid-structure interaction problems, Gas dynamics and wave propagation, Multi-scale and multiphase reactive flow, Adaptive and parallel algorithms, Mathematics for industrial applications## Selected Scholarly Works

K.B. Kiradjiev, C.J.W. Breward, I.M. Griffiths and D.W. Schwendeman, A homogenized model for a reactive filter, SIAM J. Applied Math, 81 (2021), 591-619.J.W. Banks, B.B. Buckner, W.D. Henshaw, M.J. Jenkinson, A.V. Kildishev, G. Kovacic, L.J. Prokopeva and D.W. Schwendeman, High-order accurate scheme for Maxwell's equations with a generalized dispersive material (GDM) model and material interfaces, J. Comput. Phys., 412 (2020), 109424.

F. Meng, J.W. Banks, W.D. Henshaw and D.W. Schwendeman, Fourth-order accurate fractional-step IMEX schemes for the incompressible Navier-Stokes equations on moving overlapping grids, Comput. Method. Appl. Mech. Engrg., 366 (2020), 113040.

M. Hennessey, A.K. Kapila and D.W. Schwendeman, An HLLC-type Riemann solver and high-resolution Godunov for a two-phase model of reactive flow with general equations of state, J. Comput. Phys., 405 (2020), 109180.

D.A. Serino, J.W. Banks, W.D. Henshaw and D.W. Schwendeman, A stable added-mass partitioned (AMP) algorithm for elastic solids and incompressible flow, J. Comput. Phys., 399 (2019), 108923.

D.A. Serino, J.W. Banks, W.D. Henshaw and D.W. Schwendeman, A stable added-mass partitioned (AMP) algorithm for elastic solids and incompressible flow: Model problem analysis, SIAM J. Scientific Computing, 41 (2019), A2464-A2484.

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. Phys., 378 (2019), 411-444.

J.R. Gambino, D.W. Schwendeman and A.K. Kapila, Numerical study of multiscale compaction-initiated detonation, Shock Waves, 29 (2019), 193-219.

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. Phys., 373 (2018), 455-492

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

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. Computational 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. Computational Physics, 343 (2017), 469-500.

J. Gambino, A.K. Kapila and D.W. Schwendeman, Sensitivity of run-to-detonation distance in practical explosives, Combustion Theory & 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.

D.W. Schwendeman, A.K. Kapila and W.D. Henshaw, A hybrid two-phase mixture model of detonation diffraction with compliant confinement, Comptes Rendus Mathematique, 340 (2012), 804-817.

D. Appelo, J.W. Banks, W.D. Henshaw and D.W. Schwendeman, Numerical methods for solid mechanics on overlapping grids: linear elasticity, J. Comput. Physics, 231 (2012), 6012-6050.

M. Ozlem, D.W. Schwendeman, A.K. Kapila and W.D. Henshaw, A numerical study of shock-induced cavity collapse, Shock Waves, 22 (2012), 89-117.

J.W. Banks, W.D. Henshaw and D.W. Schwendeman, Deforming composite grids for solving fluid structure problems, J. Comput. Physics, 231 (2012), pp. 3518-3547.