Vikram V Garg

Austin, Texas
Email: vikram.v.garg (at) gmail.com

CV

About

I am an applied mathematician and software engineer with strong interests in fluid mechanics and statistics. I create computational methods and algorithms to solve problems in many areas, including, the analysis of complex flows, experimental design, and density estimation. I am a developer of the Finite Element simulation library, libMesh, contributing extensively to its adaptive mesh refinement (AMR) and sensitivity analysis capabilities.


Updates:

Expertise & Accomplishments

  • Building Advanced Simulation Algorithms & Software
    • Adjoint based adaptive mesh refinement (AMR) algorithms for the variational multiscale (VMS) Finite Element Method.
    • Adjoint based, goal-oriented AMR algorithms for multiphysics flow and transport.
    • Incorporated state of the error control and automatic differentation methods in the popular C++ simulation library libMesh.
    • Added general turbulence modeling framework in the GRINS simulation library.

  • Optimization & Inference
    • Adjoint based multi-model inference algorithm which enables concurrent use of multiple physics models having varying fidelity, while guaranteeing error control.
    • Derivative based inexact constraint application methods for optimization problems with complex constraints.

  • Statistics & Data Assimilation
    • Optimal experimental design strategies for inferring high-dimensional, nonstationary ocean model parameters using R-INLA.
    • Density estimation algorithms targeted at inferring heavy tailed distributions without using specialized heuristics.
    • First fully flexible incremental Latin Hypercube sampler enabling efficient evaluation of high dimensional response functions.

Publications

Teaching

  • Massachusetts Institute of Technology
    Assistant Instructor: Computational Methods in Aeropsace Engineering - Spring 2013 & Spring 2014

  • The University of Texas at Austin
    Teaching Assistant: Freshman Calculus- Fall 2007 & Spring 2008

Service

  • Co-organizer
    Mini Symposium on "Adjoints in Computational Software" - USNCCM 2017.

  • Reviewer
    SIAM Journal on Scientific Computing, Numerische Mathematik, Computers & Mathematics with Applications, Computer Methods in Applied Mechanics & Engineering, Numerical Methods for Partial Differential Equations, International Journal for Numerical Methods in Engineering.

Education

2007 - 2012

Ph.D. in Computational and Applied Mathematics
The University of Texas at Austin
Thesis: Coupled Flow Systems, Adjoint Techniques and Uncertainty Quantification
Advisors: Graham Carey, Serge Prudhomme

2003 - 2007

B.S. in Aerospace Engineering
B.S. in Pure Mathematics

The University of Texas at Austin
GPA: 3.97/4.00

Experience