Mohsen Zayernouri

Mohsen Zayernouri

Assistant Professor, Department of Computational Mathematics, Science and Engineering; Department of Mechanical Engineering
Room 2502, Engineering Building
 428 S. Shaw Ln.
 (517) 432-0464
 zayern@egr.msu.edu

FMATH Group
FMATH Group

Scientific Leader: Dr. Mohsen Zayernouri

The overarching theme of research in Fractional Mathematics for Anomalous Transport and Hydromechanics (FMATH) Group is to bring to bear advanced computational tools from applied mathematics and data sciences to develop multi-fidelity and predictive simulation and learning tools for challenging problems, including: stochastic Lévy processes in turbulent flows, shock and interface problems in reacting and multi-phase flows, anomalous transport in porous and disordered materials, sub-/super-diffusion processes in the human brain, and complex bio-materials and tissue engineering. The main thrust of research in FMATH is on fractional-order modeling, numerical analysis (FEM, spectral methods, and spectral element methods), computational fluid dynamics, data-driven and learning algorithms for fractional PDEs, stochastic PDEs, and high performance computing.

About Me

M.Sc., 2006, mechanical engineering, Tehran Polytechnic, Iran
M.S., 2012, applied mathematics, Brown University
Ph.D., 2010, mechanical engineering, University of Utah
Ph.D., 2014, applied mathematics, Brown University

Mohsen Zayernouri is the director of the Fractional Mathematics for Anomalous Transport and Hydromechanics (FMATH) group at MSU. The overarching theme of research in FMATH is to bring to bear advanced computational tools from applied mathematics and data sciences to develop multi-fidelity and predictive simulation tools for challenging engineering problems, including: stochastic Lévy processes in turbulent flows, shock and interface problems in reacting and multi-phase flows, anomalous transport in porous and disordered materials, sub-/super-diffusion processes in the human brain, and complex bio-materials and tissue engineering. The main thrust of research in FMATH is on fractional-order modeling, numerical analysis (FEM, spectral methods, and spectral element methods), computational fluid dynamics, data-driven algorithms for fractional PDEs, stochastic PDEs, and high performance computing.

Zayernouri obtained his M.Sc. in mechanical engineering from Tehran Polytechnic, Iran. Subsequently, he joined the University of Utah, where he acquired his first Ph.D. in mechanical engineering. He then joined Brown University, where he received his second Ph.D. in applied mathematics under Professor George Em Karniadakis. Prior to joining MSU, Zayernouri was a postdoctoral research associate in the Division of Applied Mathematics at Brown University.

Research Interests

•    Numerical Analysis (FEM, spectral & spectral element methods)

•    Nonlocal Continuum Mechanics for Anomalous Transport

•    Stochastic Modeling and Uncertainty Quantification

•    Computational Fluid Dynamics

•    High Performance Computing

Selected Publications

M. Zayernouri, E. Kharazmi (2018), "Fractional Pseudo-Spectral Methods for Distributed-Order Fractional PDEs", IJCM, pg. 1-22

M. Zayernouri, M. Ainsworth, G. E. Karniadakis (2015), “Tempered Fractional Sturm--Liouville Eigen-Problems”, SIAM Journal on Scientific Computing, 37(4), A1777-A1800.

M. Zayernouri, M. Ainsworth, and G. E. Karniadakis (2015) “A Unified Petrov-Galerkin Spectral Method for Fractional PDEs”, Computer Methods in Applied Mechanics and Engineering (CMAME), 283 (1), 1545-1569.

M. Zayernouri, and G. E. Karniadakis (2015). "Fractional Spectral Collocation Methods for Linear and Nonlinear Variable Order FPDEs". Journal of Computational Physics, 293, 312-338.

... 

A Petrov–Galerkin Spectral Element Method for Fractional Elliptic Problems
July 20, 2017
A Petrov–Galerkin Spectral Element Method for Fractional Elliptic Problems

CMSE Professor Mohsen Zayernouri, the director of FMATH group, is publishing a new paper in Computer Methods in Applied Mechanics and Engineering on September 1, 2017.

Link: http://www.sciencedirect.com/science/article/pii/S0045782516312725

Petrov-Galerkin and Spectral Collocation Methods for Distributed Order Differential Equations
June 15, 2017
Petrov-Galerkin and Spectral Collocation Methods for Distributed Order Differential Equations

CMSE Professor Mohsen Zayernouri, the director of FMATH group, is publishing a new paper in SIAM Journal of Scientific Computing on 25 May 2017

Link: https://doi.org/10.1137/16M1073121 

A Review of Applications of Fractional Calculus in Earth System Dynamics
May 4, 2017
A Review of Applications of Fractional Calculus in Earth System Dynamics

CMSE Professor Mohsen Zayernouri, the director of FMATH group, has published a new paper in The Journal of Chaos, Solitons, & Fractals (2017).

Link: https://doi.org/10.1016/j.chaos.2017.03.051

CMSE faculty, M. Zayernouri, paper recognized as one the top 10 most cited JCP papers of 2014
March 22, 2017
CMSE faculty, M. Zayernouri, paper recognized as one the top 10 most cited JCP papers of 2014

M. Zayernouri & G.E. Karniadakis published a new paper in The Journal of Computational Physics, vol. 257, Part A, pp. 460–480, Jan. 2014.
DOI: 10.1016/j.jcp.2013.09.039
Link: http://www.sciencedirect.com/science/article/pii/S0021999113006530

Fractional-order uniaxial visco-elasto-plastic models for structural analysis
June 22, 2016
Fractional-order uniaxial visco-elasto-plastic models for structural analysis

CMSE Professor Mohsen Zayernouri, the director of FMATH group, has published a new paper in Computer Methods in Applied Mechanics and Engineering.

Link: doi:10.1016/j.cma.2016.05.030

A Petrov-Galerkin Spectral Method of Linear Complexity for Fractional Multi-Term ODEs on the Half Line
June 7, 2017
A Petrov-Galerkin Spectral Method of Linear Complexity for Fractional Multi-Term ODEs on the Half Line

CMSE Professor Mohsen Zayernouri, the director of FMATH group, published a new paper in SIAM Journal of Scientific Computing (SIAM J. Sci. Comput., 39(3), A922–A946) on 25 May 2017. 

Link: http://epubs.siam.org/doi/abs/10.1137/17M1113060

Teaching

FS-17: CMSE 890 Section 004 Computational Methods for Uncertainty Quantification

FS-17: ME 490 Independent Study in Mechanical Engineering

SS-18: CMSE 821 Numerical Methods for Differential Equations

Click "Teaching" link to see past courses.