Biography
Mohsen Zayernouri is the director of the Fractional Mathematics for Anomalous Transport and Hydromechanics (FMATH) group. 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.
Research interests:
- Numerical Analysis
- Uncertainty Quantification and Statistical Learning
- Fractional LES Turbulence Modeling
- Anomalous Transport
- Multiscale Material Failure Modeling
Awards
AFOSR YIP Award
ARO YIP Award
ARO MURI
NSF/DOE Award
Research Group
Education
Ph.D., 2015, Applied Mathematics, Brown University
Ph.D., 2010, Mechanical Engineering, University of Utah
M.Sc., 2012, Applied Mathematics, Brown University
M.Sc., 2006, Mechanical Engineering, Tehran Polytechnic, Iran
Publications
BOOK: M. Zayernouri, L. Wang, J. Shen, and G. E. Karniadakis, “Spectral and Spectral-Element Methods for Fractional Ordinary and Partial Differential Equations”, Cambridge University Press May 2021].
BOOK: M. Zayernouri, M. Metzger, (2013) “Computational Sensitivity Analysis of Shear Flows”, LAP LAMBERT Academic Publishing, ISBN-10: 3659454192.
BOOK CHAPTERS: A. Lischke, M. Zayernouri, Z. Zhang, (2019) “Spectral and Spectral-Element Methods for Fractional Advection-Diffusion-Reaction Equations” Handbook of Fractional Calculus with Applications. Volume 3: Numerical Methods.
BOOK CHAPTERS: M. Samiee† , E. Kharazmi† , and M. Zayernouri, (2017). “Fast Spectral Methods for TemporallyDistributed Fractional PDEs”, Selected papers from ICOSAHOM16, Springer publisher
Barros de Moraes† , E.A., Suzuki† , J.L., Zayernouri, M. (2021) Atomistic-to-Meso Multi-Scale Data-Driven Graph Surrogate Modeling of Dislocation Glide, Computational Materials Science 197, 110569.
M. Samiee† , A. Akhavan-Safaei† , and M. Zayernouri, (2020) Tempered Fractional Large Eddy Simulation: Theoretical Formulation and a Priori Study ,Journal of Fluid Mechanics, in press.
A. Akhavan-Safaei† , M. Samiee, and M. Zayernouri, (2021) Nonlocal Modeling of Turbulent Subgrid-Scale Scalar Fluxes through Fractional Operators, Journal of Computational Physics, in press.
J. L. Suzuki† , E. Kharazmi† , P. Varghaei† , M. Naghibolhosseini, M. Zayernouri, (2021) Anomalous Nonlinear Dynamics Behavior of Fractional Viscoelastic Beams, ASME Journal of Computational and Nonlinear Dynamics, in press.
E AB de Moraes, H Salehi, M Zayernouri (2020) Data-Driven Failure Prediction in Brittle Materials: A Phase-Field Based Machine Learning Framework, arXiv preprint arXiv:2003.10975.
M. Samiee, A Akhavan-Safaei, M Zayernouri, (2020) A Fractional Subgrid-scale Model for Turbulent Flows: Theoretical Formulation and a Priori Study, Journal of Physics of Fluid.
M. Samiee, E. Kharazmi, M., Zayernouri, and M. Meerschaert, (2020). Petrov-Galerkin Method for Fully Distributed-Order Fractional Partial Differential Equations. Communications on Applied Mathematics and Computation.
Y. Zhou, J. Suzuki, C. Zhang, and M. Zayernouri, (2020) Fast Implicit-Explicit Time-Integration of Nonlinear Fractional Differential Equations, Journal of Applied Numerical Mathematics.
E. Kharazmi and M. Zayernouri, (2020) Operator-Based Uncertainty Quantification of Stochastic Fractional PDEs.", ASME Journal of Verification, Validation and Uncertainty Quantification, 4-4.
E. Kharazmi and M. Zayernouri, (2019) Fractional Sensitivity Equation Method: Application to Fractional Model Construction". Journal of Scientific Computing, 80; 1, pp 110-140.
M. Ari, R. T. Faal, and M. Zayernouri, (2019) Vibrations Suppression of Fractionally Damped Plates using Multiple Optimal Dynamic Vibration Absorbers", International Journal on Computer Mathematics, pp.1-24.
M. Samiee, M. Zayernouri, and M. M. Meerschaert (2019) A Unified Spectral Method for FPDEs with Two-Sided Derivatives; Part I: A fast solver". Journal of Computational Physics, 385, 225-243.
M. Samiee, M. Zayernouri, and M. M Meerschaert, (2019) A Unified Spectral Method for FPDEs with Two-Sided Derivatives; Part II: Stability and Error Analysis. Journal of Computational Physics, 385, 244-261.
E. Kharazm, and M. Zayernouri, (2018) Fractional Pseudo-Spectral Methods for Distributed-Order Fractional PDEs. International Journal on Computer Mathematics (IJCM), 1-22, Taylor & Francis.
E. Kharazmi, M. Zayernouri, and G. E. Karniadakis, (2017) A Petrov-Galerkin Spectral-Element Method for Fractional Elliptic Problems", Journal of Computer Methods in Applied Mechanics and Engineering (CMAME), 324, 512536.
A. Lischke, M. Zayernouri, and G. E. Karniadakis, (2017) A Petrov-Galerkin Spectral Method of Linear Complexity for Fractional Multiterm ODEs on the Half-Line", SIAM Journal on Scientific Computing (SISC), 39, A922A946.
E. Kharazmi, M. Zayernouri, and G. E. Karniadakis, (2017) Petrov-Galerkin and Spectral Collocation Methods for Distributed Order Differential Equations. SIAM Journal on Scientific Computing, 39, A1003A1037.
Y. Zhang, H. Sun, H. Stowell, M. Zayernouri, and S. Hansen1 (2017) A Review of Applications of Fractional Calculus in Earth System Dynamics", Journal of Chaos, Solitons, and Fractals,102, 29-46.
M. Zayernouri and A. Matzavinos. Fractional Adams-Bashforth/Moulton Methods: An Application to the Fractional Keller-Segel Chemotaxis System. Journal of Computational Physics, 317 (2016): 1-14.
J. L. Suzukiz, M. Zayernouri, M. L. Bittencourt, M. L., and G. E. Karniadakis, (2016). Fractional- order Uniaxial Visco-Elasto-Plastic Models for Structural Analysis. Computer Methods in Applied Mechanics and Engineering,308, 443-467.
M. Zayernouri, M. Ainsworth, and 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.
M. Zayernouri, G. E. Karniadakis (2014) “Exponentially Accurate Spectral and Spectral Element Methods for Fractional ODEs”, Journal of Computational Physics, 257, 460–480.
M. Zayernouri, G. E. Karniadakis (2014) “Fractional Spectral Collocation Method”, SIAM Journal on Scientific Computing, 36 (1), A40–A62.
M. Zayernouri, G. E. Karniadakis (2014) “Discontinuous Spectral Element Methods for Time- and Space-Fractional Advection Equations”, SIAM Journal on Scientific Computing, 36 (4), B684–B707.
M. Zayernouri, W. Cao, Z. Zhang, G. E. Karniadakis (2014) “Spectral and Discontinuous Spectral Element Methods for Fractional Delay Equations”, SIAM Journal on Scientific Computing, 36 (6), B904-B929.
M. Zayernouri, G. E. Karniadakis (2013) “Fractional Sturm-Liouville Eigen-Problems: Theory and Numerical Approximations”, Journal of Computational Physics, 47-3, 2108–2131.
M. Zayernouri, S. W. Park, D. M. Tartakovsky, and G. E. Karniadakis (2013) “Stochastic Smoothed Profile Method for Modeling Random Roughness in Flow Problems”, Computer Methods in Applied Mechanics and Engineering (CMAME), 263, 99-112.
M. Zayernouri and M. M. Metzger (2011) “Coherent Features in the Sensitivity Field of a Planar Mixing Layer”, Physics of Fluid, 23, 025105.
M. J. Kermani, M. Zayernouri, and M. Saffar-Avval (2007) “Generalization of a Two-Phase Steam Flow Calculator to High-Pressure Cases; an Analytical Approach,” Canadian Journal of Mechanical Engineering: Transaction of the CSME, Vol. 30 (4), 581-595.
M. Zayernouri, and M. J. Kermani (2006) “Development of an Analytical Solution for Compressible Two-Phase Steam Flow,” Canadian Journal of Mechanical Engineering: Transaction of the CSME, Vol. 30 (2), 279-296.
Primary Department
