##### KMap

#### VOSviewer

##### 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

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