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Courses
- MPNAMathematical Principles of Numerical Analysis
- CSAMCase Studies in Applied Mathematics
- CIICalculus II
- PDEPartial Differential Equations
- AAMAdvanced Applied Mathematics
- NANumerical Analysis
- MAEMathematical Analysis for Engineers
- NAPDENumerical Analysis PDE
- SMSAStatistical Methods in Sports Analytics
Grants
- Mathematical Modeling and Data Analysis (WAESO)
Principal Investigator (PI)
2015
$371.9
- Collaborative Research: Wavelet Frames for Variational Models in Imaging: Bridging Discrete and Continuum
Principal Investigator (PI)
2014
$170.8K
- Invisible Cloaking and Local Mesh Refinement: Novel Applications of Transformation Optics (WAESO)
Principal Investigator (PI)
2014
$378.0
- Modeling and optimization of ultrashort laser pulse energy deposition (WAESO)
Principal Investigator (PI)
2014
$378.0
- Application of Adaptive Meshes and Transformation Optics to Maxwell Solvers (WAESO)
Principal Investigator (PI)
2014
$373.9
- Mathematical Modeling and Simulations
Principal Investigator (PI)
2013
$756.0
- Laser Ablation of thin films, Surgery and Statistical analysis validation (WAESO)
Principal Investigator (PI)
2013
$756.0
- Mathematical Modeling, Computer Simulations and Experiments in Laser Induce
Principal Investigator (PI)
2013
$378.0
- (BRI) Unified First-Prinicple Analysis of Ultraintense Laser-Matter Interactions: Theory, Computation and Experiments
Co-Investigator (COI)
2012
$1.5M
- Topics in Computational Mathematics (WAESO)
Principal Investigator (PI)
2012
$756.0
Publications (54)
Recent
- FDTD Method With Explicit Non-Iterative and Second Order Treatment for Kerr Nonlinearities
2022
- Optimal parameter selection in Week's method for numerical Laplace transform inversion based on machine learning
2021
- Spectral solution of PDEs on networks
2021
- Scattering of a short electromagnetic pulse from a Lorentz–Duffing film: Theoretical and numerical analysis
2019
- Second-order, stable, fully anisotropic FDTD
2019
- Exponential time-differencing with embedded Runge-Kutta adaptive step control
2015
- Finite-Difference Time-Domain simulatio n of spacetime cloak
2014
- Transformation optics based local mesh refinement for solving Maxwell's equations
2014
- An overlapping Yee finite-difference time-domain method for material interfaces between anisotropic dielectrics and general dispersive or perfect electric conductor media
2014
- Anisotropic terahertz response from a strong-field ionized electron-ion plasma
2013
- Subpixel smoothing finite-difference time-domain method for material interface between dielectric and dispersive media
2012
- Dempster-Shafer evidential theory for the automated selection of parameters for Talbot's method contours and application to matrix exponentiation
2012
- Generalization of the FDTD algorithm for simulations of hydrodynamic nonlinear Drude model
2010
- Application of Post's formula to optical pulse propagation in dispersive media
2010
- A diagonal split-cell model for the overlapping Yee FDTD method
2009
- Overlapping Yee FDTD method on nonorthogonal grids
2009
- Analysis of the analytic dispersion relation and density of states of a selected photonic crystal
2008
- Numerical grid generation
2008
- Bibliography
2008
- Preface
2008
- Overview of partial differential equations
2008
- Problems with multiple temporal and spatial scales
2008
- Discretization methods
2008
- Numerical boundary conditions
2008
- Convergence theory for initial value problems
2008
- Multimode interference in circular step-index fibers studied with the mode expansion approach
2007
- The Maxwell-Lorentz model for optical pulses
2007
- Second-order accurate FDTD space and time grid refinement method in three space dimensions
2006
- Kink shape solutions of the Maxwell-Lorentz system
2005
- A mixed high-order vector finite element method for waveguides: Convergence and spurious mode studies
2005
- Application of the Finite-Difference Time-Domain method with local grid refinement to nanostructure design
2005
- Variational principles, Lie point symmetries, and similarity solutions of the vector Maxwell equations in non-linear optics
2004
- Numerical simulations of active microstructured fibers
2004
- AMR FDTD solver for nanophotonic and plasmonic applications
2004
- Slab delivery of incoherent pump light to double-clad fiber amplifiers: Numerical simulations
2004
- Solitary waves, steepening and initial collapse in the Maxwell-Lorentz system
2002
- Erratum: Steady MHD flows with an ignorable coordinate and the potential transonic flow equation (Journal of Plasma Physics (1994) 52 (141-188))
2001
- Two-Dimensional Riemann Solver for Euler Equations of Gas Dynamics
2001
- Parametric instabilities and wave coupling in Alfvén simple waves
2001
- Nonlinear and three-wave resonant interactions in magnetohydrodynamics
2000
- Weak shock reflection
2000
- The von Neumann paradox in weak shock reflection
2000
- Wave interactions in magnetohydrodynamics, and cosmic-ray-modified shocks
1999
- Multidimensional simple waves in gas dynamics
1998
- Lagrangian and Hamiltonian aspects of wave mixing in non-uniform media: Waves on strings and waves in gas dynamics
1998
- Hamiltonian aspects of three-wave resonant interactions in gas dynamics
1997
- Wave-wave interactions in two-fluid cosmic-ray hydrodynamics
1997
- Lie-Bäcklund symmetries of dispersionless, magnetohydrodynamic model equations near the triple umbilic point
1996
- Evolutionary Bidomain model of the continuous excitable medium
1996
- Contact and pressure balance structures in two-fluid cosmic-ray hydrodynamics
1995
- Asymptotic equations for conservation laws of mixed type
1992
- Mach reflection for the two-dimensional Burgers equation
1992
- An upwind differencing scheme for the equations of ideal magnetohydrodynamics
1988
- Propagation of weakly nonlinear magnetoacoustic waves
1987