Research

I'am currently at Michigan State University (MSU). I am working as a postdoctoral research associate with Prof. Shanker Balasubramaniam in the general area of computational electromagnetics and sciences. I defended my Ph.D. in electrical engineering (Dept. of ECE, MSU) on Dec.12,2008 under the guidance of Prof. Shanker Balasubramaniam and officially graduated in May 2009.
My research work focusses on the development of algorithms for fast computation of different potentials for simulation in time and frequency domains. This serves as the basis for development of fast and efficient solvers and simulation tools with variety of applications. These include the modeling of electromagnetic (EM) field interaction with large aircraft bodies to Terahertz devices that exhibit multi-scale features, multi-physics simulations like molecular dynamics and diffusion phenomena.

Following is a brief listing of my research and research interests( CV , Resume ) :

Thesis work

Fast Computational methods: Computational Electromagnetics (CEM)
(Computational Electronics, Molecular Dynamics )
- Fast Multipole Methods (FMM)
- Accelerated Cartesian Expansions (ACE)
- Fast Kernels/potentials developed with ACE:
  - Helmholtz (Wideband): freq. domain wave eq.
  - Retarded : time domain wave eq.
  - Diffusion: time domain diffusion equation
  - London potentials: large scale molecular dynamics (Fast Parallel FMM code is being embedded with LAMMPS or NAMD)
- Scalable parallel FMM/Tree codes
  (shown scalability from 32 to 1024 processors with 97% efficieny !!)
Integral equation modeling for (CEM):
- Fast solutions for multiscale problems (using wideband ACE+FMM)
- Stable and Well-Conditioned formulations
- Fast IE models to simulate Eddy current testing (ECT) for defects in planar-layered medium
Applications:
- Wideband electromagnetic simulations: antennas, feed structures, scattering (time and freq.)
- Molecular dynamics : large scale simulations with parallelization
- Computational Electronics : Quantum scale and macro-scale
Other interests
Inverse problems : application to NDE, process and design optimization
Signal and Image Processing
NDE techniques: Ultrasonics, Eddy current, Microwave, Terahertz and more....
Patterm Recognition, Classification
Chaos and Fractals: applications (informal/personal attraction in science)

Journal Publications:

M. Vikram , P. Chahal and B. Shanker, "Numerical methods for desgin and optimization of Terahertz devices", in preparation
M. Vikram and B. Shanker, "Fast EM solver for complex multiscale geometries", in preparation
M. Vikram , B. Shanker and S. Aluru,"Scalable parallel EM solvers", in preparation
M. Vikram , C. Knowles, B. Shanker and L. Kempel, "Ultra-wideband (UWB) FMM", in preparation
M Vikram, B. Shanker and S. Aluru, “Provably Optimal Parallel Algorithms for Large Scale Parallelization of FMM based EM Solvers”, in preparation for IEEE Trans. Antennas and Propagat.
M Vikram, A. Baczewski, B. Shanker and L. Kempel, “Novel Methods for Rapid solution of time domain diffusion equation”, under review, Journal of computational physics, October 2008.
M Vikram, H. Huang, B. Shanker and T. Van, “ A Novel Wideband FMM for Fast Integral Equation Solution of Multiscale Problems in Electromagnetics ”, to appear in IEEE Trans. Antennas and Propagat., (Accepted Dec. 2008).
M. Vikram, B. Shanker, “An incomplete review of fast multipole methods-from static to wideband-as applied to problems in computational electromagnetics”, to appear in Journal of Applied Computational Electromagnetic Society (Accepted Sept. 2008).
M. Vikram, B. Shanker, “Fast Evaluation of Time Domain Fields in Sub-Wavelength Source/Observer Distributions using Accelerated Cartesian Expansions (ACE)”, Journal of Computational Physics, Vol. 227, Issue 2, pp. 1007-1023, Dec. 2007.
K. Arunachalam, V. R. Melapudi, L. Udpa, and S. S. Udpa, “Microwave NDT of Cement-Based Materials Using Far Field Reflection Coefficients”, NDT and E International, Vol. 39, pp. 585-593, 2006.
N. V. Nair, V. R. Melapudi, H. R. Jimenez, X. Liu, Y. Deng, Z. Zeng, L. Udpa, T. J. Moran, and S. S. Udpa, “A GMR-Based Eddy Current System for NDE of Aircraft Structures”, IEEE Transactions on Magnetics, Vol. 42, Issue 10, pp. 3312-3314, Oct. 2006.

Contact:
Email: vikramr@msu.edu
2120, Engg. building
Dept. of ECE
East Lansing
MI 48824, USA