Research Interests

• Computational acoustics and electromagnetics
  • Forward and Inverse problems for (dispersive) wave phenomena
  • Homogenization of Maxwell's equations
  • Perfectly matched layers
• Parameter estimation, statistical inference and optimization techniques
• Fictitious domain (domain imbedding) methods, finite difference methods, finite element methods, operator splitting schemes
• Structured population models, infectious disease dynamics, semigroup theory

• Curriculum Vita
• Research Statement
• Teaching Statement

  Reports and Publications

  • H. T. Banks, V. A. Bokil and S. Hu, Monotone Approximation for a Nonlinear Size and Age Structured Epidemic Model, To appear in Nonlinear Analysis: Real World Applications. Also, Tech. Rep. CRSC-TR06-09, Center for Research in Scientific Computation, North Carolina State University, Jan, 2006.
  • V. A. Bokil and R. Glowinski, A Distributed Lagrange Multiplier Based Fictitious Domain Method for Maxwell's Equations, To appear in International Journal of Computational and Numerical Analysis and Applications. Also, Tech. Rep. CRSC-TR06-04, Center for Research in Scientific Computation, North Carolina State University, Jan, 2006
  • 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, To appear in Mathematical Biosciences and Engineering. Also, Tech. Rep. CRSC-TR05-45 Center for Research in Scientific Computation, North Carolina State University, Dec, 2005.
  • G. M. Kepler, R. A. Albanese, H. T. Banks, and V. A. Bokil, Reflection of Microwave pulses from acoustic waves: Summary of experimental and computational studies, Tech. Rep. CRSC-TR05-23, Center for Research in Scientific Computation, North Carolina State University, May, 2005.
  • H. T. Banks, V. A. Bokil, D. Cioranescu, N. L. Gibson, G. Griso, and B. Miara, Homogenization of Periodically Varying Coefficients in Electromagnetic Materials, Tech. Rep. CRSC-TR05-05, Center for Research in Scientific Computation, North Carolina State University, January 2005. To appear in Journal of Scientific Computing.
  • H. T. Banks, and V. A. Bokil, A Computational and Statistical Framework for Multidimension Domain Acoustooptic Material Interrogation, in Quarterly of Applied Mathematics, Volume LXIII, Number 1, March 2005, Pages 156-200. Also Tech. Rep. CRSC-TR04-27b
  • 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 fictitious domain method with operator splitting for wave problems in mixed form, in Mathematical and numerical aspects of wave propagation---WAVES 2003, 437--442, Springer, Berlin, 2003.
  • H. T. Banks, and V. A. Bokil, Parameter Identification for dispersive dielectrics using pulsed microwave interrogating signals and acoustic wave induced reflections in two and three dimensions, Tech. Rep. CRSC-TR04-27, Center for Research in Scientific Computation, North Carolina State University, July, 2004.
  • V. A. Bokil, Computational Methods for Wave Propagation Problems on Unbounded Domains (8Mb), PhD Thesis, Department of Mathematics, University of Houston, May 2003

  Presentations

  • 8th US National Congress on Computational Mechanics, Austin, TX, A Fictitious Domain Method with Operator Splitting and Perfectly Matched Layers for Wave Propagation Problems Domain Decomposition and Fictitious Domain Methods, organized by I. Herrera and R. Glowinski, July 24-28, 2005
  • Sixth SIAM Conference on Control and its Applications, New Orleans, LA. Parameter Estimation for Electromagnetic Materials using Homogenization of Periodically Varying Coefficients, Inverse Problems in Electromagnetics and Biology Minisymposium, organized by H. T. Banks and A. S. Ackleh, July 2005.
  • 29th Annual SIAM Southeast Atlantic Section Meeting, Charleston, SC. Parameter Identification for Dispersive Dielectrics using Acoustooptic Material Interrogation, Inverse Problems in Electromagnetics and Biology Minisymposium, organized by H. T. Banks and N. L. Gibson, March 2005.

  Work in Progress

  • Homogenization of Electromagnetic Materials
  • Wave Propagation in Dispersive Media: finite element methods, inverse problems
  • Weak formulations and nonlinear semigroups for structured epidemic models
  • Perfectly matched layer models: finite element methods