List of Publications

Publications (reverse chronological order)

  1. M. K. Ballard, R. Amici, V. Shankar, L. A. Ferguson, M. Braginsky, and R. M. Kirby. Towards an Extrinsic, CG-XFEM Approach Based on Hierarchical Enrichments for Modeling Progressive Fracture (Submitted to Computer Methods in Applied Mechanics and Engineering, April 2021).[link][preprint] 

  2. H. Elich, A. Barrett, V. Shankar, and A. L. Fogelson. Pump efficacy in a fluid-structure-interaction model of a chain of contracting lymphangions (Under revision, 2021). [link][preprint]

  3. V. Shankar, G. B. Wright, and A. L. Fogelson. An Efficient High-Order Meshless Method for Advection-Diffusion Equations on Time-Varying Irregular Domains (Under revision, 2021). [link][preprint]

  4. A. Kassen, V. Shankar, and A. L. Fogelson. A fine-grained parallelization of the Immersed Boundary method (Under revision, 2021). [link][preprint]

  5. V. Shankar, G. B. Wright, and A. Narayan. A Robust Hyperviscosity Formulation for Stable RBF-FD Discretizations of Advection-Diffusion-Reaction Equations on Manifolds (SIAM Journal on Scientific Computing, August 2020).[link][preprint]

  6. Sean D. Lawley and V. Shankar. Asymptotic and numerical analysis of a stochastic PDE model of volume transmission (SIAM Multiscale Modeling and Simulation, May 2020). [link][preprint] 

  7. M.K. Ballard, R. Amici, V. Shankar, and R.M. Kirby. A preliminary assessment of a new XFEM framework for predicting complex fracture (ICCM22, 2019). [link]

  8. V. Shankar and A. L. Fogelson. Hyperviscosity-based Stabilization for Radial Basis Function-Finite Difference (RBF-FD) discretizations of advection-diffusion equations (Journal of Computational Physics, November 2018). [link][preprint]

  9. V. Shankar, A. Narayan, and R. M. Kirby. RBF-LOI: Augmenting Radial Basis Functions (RBFs) with Least Orthogonal Interpolants (LOI) for Solving PDEs on Surfaces (Journal of Computational Physics, November 2018). [link][preprint]

  10. V. Shankar and G. B. Wright. Mesh-free Semi-Lagrangian Methods for Advection on a Sphere using Radial Basis Functions (Journal of Computational Physics, August 2018). [link][preprint]

  11. V. Shankar, A. L. Fogelson and R. M. Kirby. Robust Node Generation for Meshfree Discretizations on Irregular Domains and Surfaces (SIAM Journal on Scientific computing, August 2018). [link][preprint]

  12. S. Pokhrel, V. Shankar and J. J. Simpson. 3-D FDTD Modeling of Electromagentic Wave Propagation in Magnetized Plasma Requiring Singular Updates to the Current Density Equation (IEEE Transactions on Antennas and Propagation, June 2018). [link]

  13. V. Zala, V. Shankar, S. P. Sastry and R. M. Kirby. Curvilinear Mesh Rectification using Radial Basis Function Interpolation and Smoothing (Journal of Scientific Computing, 2018). [link][preprint]

  14. S. Pokhrel, V. Shankar and J. J. Simpson. Simplified FDTD model of electromagnetic wave propagation in magnetized plasma (Applied Computational Electromagnetic Society Symposium [ACES], March 2018). [link]

  15. V. Shankar. The Overlapped Radial Basis Function-Finite Difference (RBF-FD) Method: A Generalization of RBF-FD (Journal of Computational Physics, August 2017). [link][preprint]

  16. E. Lehto, V. Shankar and G. B. Wright. A Radial Basis Function (RBF)-Based Compact Finite Difference (FD) Scheme for Reaction-Diffusion Equations on Surfaces (SIAM Journal on Scientific Computing, September 2017). [link][preprint]

  17. E. Fuselier, V. Shankar and G. B. Wright. A Radial Basis Function (RBF)-Based Leray Projection Method for the Incompressible Unsteady Stokes Equations (Computers and Fluids, April 2016). [link][preprint]

  18. V. Shankar, G. B. Wright, R. M. Kirby and A. L. Fogelson. Augmenting the Immersed Boundary method with Radial Basis Functions (RBFs) for the simulation of platelets in hemodynamic flows (Int. J. for Numerical Methods in Fluids, July 2015). [link][preprint]

  19. V. Shankar and S. D. Olson. Radial Basis Function (RBF)-based Parametric Models for Closed and Open Curves within the Method of Regularized Stokeslets (Int. J. for Numerical Methods in Fluids, May 2015). [link][preprint]

  20. V. Shankar, G. B. Wright, R. M. Kirby and A. L. Fogelson. A Radial Basis Function (RBF)- Finite Difference (FD) method for diffusion and reaction-diffusion equations on surfaces (Journal of Scientific Computing, September 2014). [link][preprint]

  21. V. Shankar, G. B. Wright, A. L. Fogelson and R. M. Kirby. A Radial Basis Function (RBF) Finite Difference method for the simulation of reaction-diffusion equations on stationary platelets within the augmented forcing method (Int. J. for Numerical Methods in Fluids, Jan 2014). [link][preprint]

  22. V. Shankar, G. B. Wright, A. L. Fogelson and R. M. Kirby. A study of different modeling choices for simulating platelets within the Immersed Boundary method (APNUM, Jan 2013). [link][preprint]

PhD Dissertation

V. Shankar. Radial Basis Function-Based Numerical Methods For The Simulation Of Platelet Aggregation (PhD thesis/dissertation). [link]