Robert Krasny

Arthur F. Thurnau Professor
Department of Mathematics
4830 East Hall
530 Church Street
University of Michigan
Ann Arbor, MI 48109-1043
phone: (734)-763-3505
fax: (734)-763-0937
email: krasnyATumichDOTedu

Applied Honors Calculus at Michigan

fast adaptive particle methods and applications

electrostatics

polar vortex

DPP talk

two-stream instability

teaching

fall 2024

Math 156 Applied Honors Calculus II

winter 2025

Math 572 Numerical Methods for Differential Equations

Math 371 Numerical Methods for Engineers

Math 471 Numerical Methods

Math 557 Methods of Applied Mathematics II: Asymptotics

Math 558 Applied Dynamical Systems

Math 571 Numerical Linear Algebra

Math 654 Introduction to Fluid Dynamics

Math 655 Topics in Fluid Dynamics - Hydrodynamic Stability

Math 671 Topics in Scientific Computing: Particle Methods

Math 671 Topics in Scientific Computing: Wavelets

research

scientific computing, particle methods, integral equations
1. fluid dynamics, vortex dynamics, Kelvin-Helmholtz instability, vortex sheet roll-up, vortex rings, vortex dipoles, aircraft wake structure, Hamiltonian chaos in vortex flow
2. tree-based fast summation methods for long-range particle interactions, barycentric Lagrange treecode and dual tree traversal method, parallel implementation on CPU clusters and GPUs
3. electrostatics of solvated biomolecules, boundary integral method for Poisson-Boltzmann implicit solvent model
4. geophysical fluid flow, particle method for barotropic vorticity equation on a rotating sphere
5. electronic structure, integral equation based method for Kohn-Sham density functional theory
6. plasma dynamics, particle method for Vlasov-Poisson system
profile
publications
picture gallery of vortex motion

fast summation software

Nathan Vaughn, Leighton Wilson BaryTree library
Keith Lindsay regularized Biot-Savart interaction, free-space BC, written in C
Zhong-Hui Duan Coulomb interaction, periodic BC (Ewald/treecode for real space sum), written in C
Hans Johnston Coulomb and screened Coulomb interactions, free-space BC, written in Fortran90
Henry Boateng particle-cluster and cluster-particle treecodes, Coulomb interaction, free-space BC, disjoint targets and sources, written in Fortran90
Weihua Geng boundary integral Poisson-Boltzmann solvers

data

travel

links

AIM - Applied and Interdisciplinary Mathematics at the University of Michigan
Michigan Center for Computational Medicine and Bioinformatics
Michigan Center for Theoretical Physics
Michigan Institute for Plasma Science and Engineering
Fellowships, Workshops, etc. for students and postdocs
SIAM Society for Industrial and Applied Mathematics
JJIAM Japan Journal of Industrial and Applied Mathematics
History of Numerical Analysis and Scientific Computing, articles and interviews collected by SIAM
career webpage from SIAM
career brochure from SIAM
HPCwire Job Bank

This material is based upon work supported by the National Science Foundation under Grant No. 0510162. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.