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Rajat Arora

About Me

Hello, I'm Rajat. I am currently working as an Research Scientist at Siemens. I graduated with a Ph.D. in the field of Computational Mechanics from Carnegie Mellon University (CMU). My research focused on numerical analysis, material science, and scientific software development.

Education

Jun'15 - Feb'19

Ph.D.

Carnegie Mellon University

Computational Mechanics GPA: 4.0/4.0

  • Mathematics of Finite Element Method
  • Differential Geomtery for Mechanics
  • Computational Modeling of Materials
  • Dislocation based Plasticity
  • Real Analysis II
Jun'15 - Dec'17

Master of Science

Carnegie Mellon University

Computational Mechanics GPA: 4.0/4.0

  • Real Analysis I
  • Mathematical Methods in Engineering
  • Fundamental Concepts and Methods of Structural Mechanics
  • Numerical Methods in Engineering
  • Molecular Dynamics
Jan'13 - Oct'14

Master of Technology

Indian Institute of Technology Kanpur (IITK)

Mechanical Engineering GPA: 9.7/10.0

  • Advanced Finite Element Method
  • Advanced Mechanics of Solids
  • Theory of Plasticity
  • Thermodynamics of Continous Media
July'09 - Dec'12

Bachelor of Technology

Indian Institute of Technology Kanpur (IITK)

Mechanical Engineering GPA: 8.3/10.0

  • Ordinary and Partial Differential Equations
  • Complex Analysis & Linear Algebra
  • Introduction to Solid Mechanics
  • Heat and Mass Transfer
  • Fluid Mechanics
2006 - 2008

High School

I completed my high school from Kids Corner Senior Secondary School, Firozabad in May 2008.

MY Skills

  • Knowledge of finite element methods for PDE discretizations on unstructured meshes: Galerkin FEM, Least Squares FEM, Galerkin-Least Squares FEM, Discontinuous-Galerkin FEM
  • Experience with Object Oriented Design concepts, the Message Passing Interface (MPI) library, and multithreading using OpenMP
  • Knowledge of C++, Python, and MATLAB and experienced in developing complex scientific software on Unix-based platforms
  • Experience with Computational paradigms such as Automatic Differentiation (Sacado) and automated code generation using template based programming
  • Proficient verbal and written communication skills necessary to interact with a multi-disciplinary research team
MPI
C/C++
MATLAB
Python
OpenMP

  • Experience with Adaptive Mesh Refinement (AMR) on unstructured meshes
  • Best practices in software development including unit tests, coding practices
  • Authored technical and scientific reports and papers, and delivered scientific presentations


Experience with

  • Deal.ii FEA subroutines
  • PETSc Linear Algebra and Solver package
  • GIT: Version control software
  • Software collaboration platforms such as GitHub

Familiar with

  • Isogeometric Analysis
  • Code documentation using Doxygen
  • Cubit Meshing program
  • Visualization using post-processing program such as Paraview

Relevant Coursework

  • Finite Element Method
  • Advanced Finite Element Method
  • Theory of Plasticity
  • Advanced Mechanics of Solids
  • Computational Modeling of Materials
  • Dislocation Mechanics
  • Ordinary and Partial Differential Equations
  • Thermodynamics of Continuous Media
  • Mathematics of Finite Element Method
  • Numerical Methods in Engineering
  • Differential Geometry for Mechanics
  • Fracture & Fatigue
  • Molecular Simulation of Materials
  • Principles of Real Analysis I
  • Principles of Real Analysis II

I What I Do

MY Projects

This is a list of several of my projects over the last couple years!


Microstructure development in simpleshear

Computational Approximation of Mesoscale Field Dislocation Mechanics (MFDM) at Finite Deformation

June'15 - Feb'19 Ph.D. Dissertation at CMU

This research focused on developing a massively parallel finite element based theoretical-computational framework for finite deformation MFDM theory to study plastic deformation in materials; Used: MPI, Deal.ii, PetSc, and P4est.

Precipitate Evolution

Shape Evolution of Precipitates using Extended Finite Element Method Coupled with Level Set Method

May'13 - Oct'14 Master's Dissertation at IITK

This research focused on analyzing the morphological evolution of arbitrarily shaped precipitates embedded coherently in a matrix. I developed a C++ code that used Extended Finite Element Method (XFEM) coupled with PDE based narrow band Level Set Method (LSM) to capture motion of the interface as the precipitate evolves.

Elasto-Plastic Modeling

Modeling Elastic-Plastic Deformation

Aug'15 - Dec'15 Course Project

I developed a C++ code employing finite element method (FEM) to analyze elasto-plastic deformation of a 2D plate under plane strain conditions using J2 plasticity theory along-with non-linear isotropic hardening.

Crack opening in Mode I

Modeling Crack using Extended Finite Element Method

Mar'14 - Apr'14 Course Project

Modeled opening of a crack in a finite 2D plate under uniaxial tension using Extended Finite Element Method (XFEM) and Linear Elastic Fracture Mechanics (LEFM).

Bifurcation in Precipitate Shape Evolution

Elastically Induced Shape Bifurcation of Inclusions

Jan'13 - Apr'13 Course Project

Examined transitions in equilibrium shape of a precipitate, embedded coherently in a matrix, for isotropic systems under plane-strain conditions, as a function of various parameters: size of particle, mismatch, external stress, elastic and interfacial energies.

Beam at Large rotations and small Strains

Nonlinear Modeling of Beam Bending at Large Deformation

Mar'13 - Apr'13 Course Project

Developed an FEM code to simulate beam bending using Total Lagrangian formulation with von Karman strains and compared various mathematical iterative schemes (Picard's method, Newton-Raphson method, Arc Length method) to obtain solution to nonlinear equations.

Field variable disconitnuous at the interface

Discontinuous Galerkin Method

Nov'17 - Dec'17 Independent Project

Implemented Discontinuous Galerkin Finite element method to solve a steady-state advection equation.

Motion of a localized dislocation core

Solving Convection-Diffusion Equation

Apr'18 - Aug'18 Independent Project

Implemented Local Discontinuous Galerkin (LDG) Method to solve an unsteady convection-diffusion equation.

Isogeometric Analysis

Jan'18 - Mar'18 Independent Project

Learned and Implemented Isogeometric Analysis to solve Laplace equation in a 2d domain.

Automatic Differentiation

Oct'17 Independent Project

Employed Automatic Differentiation (Sacado) to solve a non-linear minimal surface equation.

Adaptive Mesh Refinement (AMR)

Jul'17 - Aug'17 Independent Project

Implemented Adaptive Mesh Refinement (AMR) to perform multiple levels of mesh refinement/coarsening to resolve the interfaces between different materials in the mesh. Used it to get the outlines of geographic map of India starting from a png image.