- 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.
- 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.
- 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
- 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).
- 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.
- 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.
- 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.
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.