Research Interests

• Numerical Analysis and
• Scientific Computing
  

My primary research interests include:

• Numerical methods for computational electromagnetics. Specifically numerical methods for forward and inverse problems
  for (dispersive) wave phenomena.
  • finite difference and finite element methods
  • operator splitting techniques
  • fictitious domain methods
• Homogenization of Maxwell's equations in dispersive dielectrics.
• Construction and discretization of perfectly matched layers for CEM.
• Parameter estimation, statistical inference and optimization techniques.
• Mathematical Modeling of infectious diseases, including structured population models.

Grant Funding

Refereed Publications

• H. T. Banks, V. A. Bokil and N. L. Gibson, Analysis of Stability and Dispersion in a Finite Element Method for Debye and Lorentz Media,
  Numerical Methods for Partial Differential Equations, accepted .
• H. T. Banks, V. A. Bokil and N. L. Gibson, Parameter Estimation Versus Homogenization Techniques in Time-Domain Characterization
  of Composite Dielectrics in Journal of Inverse and Ill Posed Problems, 15(2), 117-135, 2007.
• V. A. Bokil and M. W. Buksas, Comparison of Finite difference and Mixed Finite Element Methods for Perfectly Matched Layer Models,
  Communications in Computational Physics, 2(4), 806-826, 2007.
• H. T. Banks, V. A. Bokil and S. Hu, Monotone Approximation for a Nonlinear Size and Age Structured Epidemic Model,
  Nonlinear Analysis: Real World Applications, 8(3), 834--852, 2007.
• H. T. Banks, V. A. Bokil, S. Hu, A. K. Dhar, R. A. Bullis, C. L. Browdy and F.C.T. Allnutt, Modeling Shrimp Biomass and Viral Infection
  for Production of Biological Countermeasures, Mathematical Biosciences and Engineering, 3(4), 635--660, Oct 2006.
• H. T. Banks, V. A. Bokil, D. Cioranescu, N. L. Gibson, G. Griso, and B. Miara, Homogenization of Periodically Varying Coefficients
  in Electromagnetic Materials, Journal of Scientific Computing, 28(2-3), 191--221, Aug 2006
• H. T. Banks, and V. A. Bokil, A Computational and Statistical Framework for Multidimension Domain Acoustooptic Material Interrogation,
  Quarterly of Applied Mathematics, Volume LXIII, Number 1, March 2005, Pages 156-200.
• V. A. Bokil and R. Glowinski, An Operator Splitting Scheme with a Distributed Lagrange Multiplier Based Fictitious Domain Method for
  Wave Propagation Problems, in J. Comp. Phys., 205 (2005), 242--268.
• V. A. Bokil and R. Glowinski, A Distributed Lagrange Multiplier Based Fictitious Domain Method for Maxwell's Equations,
  International Journal of Computational and Numerical Analysis and Applications, 6(3), 203--245, 2004.
• V. A. Bokil and R. Glowinski, A fictitious domain method with operator splitting for wave problems in mixed form,
  Mathematical and numerical aspects of wave propagation WAVES 2003, 437--442, Springer, Berlin, 2003.
• V. A. Bokil, Computational Methods for Wave Propagation Problems on Unbounded Domains (8Mb),
  PhD Thesis, Department of Mathematics, University of Houston, May 2003

Recent Presentations

• Analysis of Stability and Dispersion in a Finite Element Method for Debye and Lorentz Dispersive Media
  AWM Workshop for Women Graduate Students and Recent PhDs, San Diego, CA, July 6-9, 2008.
• Introduction to the Mathematics of Infectious Diseases
  2007 REU Program in Mathematics at Oregon State University, August 2007
• Introduction to Finite Difference, Finite Element and Finite Volume Methods for the Numerical Solution of Partial Differential Equations
  2007 Summer School on Multiscale Mathematics and High Performance Computing, June 30, 2007
• Numerical Solution of a Homogenization Model for Spatially Periodic Dispersive Dielectrics
  Modeling, Analysis and Simulation of Multiscale Nonlinear Systems Workshop at Oregon State University, Corvallis, OR, June 29, 2007.
• Operator Splitting Schemes, Distributed Lagrange Multiplier Based Fictitious Domain Methods and Perfectly Matched Layers for Wave Propagation Problems.
  Applied Mathematics and Computation Seminar, Department of Mathematics, Oregon State University, Corvallis, OR, Jan 12, 2007.

Work in Progress

• Operator Splitting Methods for Electromagnetic Wave Propagation in Dispersive Dielectrics.
• Theoretical Analysis of an Acoustooptic Interrogation Model using Energy Methods
• Homogenization of Electromagnetic Materials using Stable higher Order Polarization Laws.
• Mathematical Modeling of Invasive Species and Diseases in Metapopulations.
• Mathematical and Numerical Analysis of Reactive Transport in Discontinuous Porous Media.

Conferences and Workshops Recently Attended

• SIAM Annual Meeting, July 7-11, 2008, San Diego, CA.
• AWM Workshop for Women Graduate Students and Recent PhDs , San Diego, CA, July 6-9, 2008.
• Workshop on High-order methods for computational wave propagation and scattering , American Institute of Mathematics, Palo Alto, Sept 10-14, 2007
• Multiscale Mathematics and High-Performance Computing Summer School, Oregon State University, 29 June - 3 July, 2007.
• Workshop on Modeling, Analysis and Simulation of Multiscale Nonlinear Systems, Oregon State University, June 25-29, 2007.