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Rajat Arora

About Me

Hello, I'm Rajat. I am a Ph.D. candidate in the field of Computational Mechanics at Carnegie Mellon University (CMU). My current research focuses on numerical analysis, material science, and scientific software development.

My interests lie in the broad area of theoretical and applied mechanics, and development and use of advanced modeling methods to study macroscopic mechanical response of materials. I am also interested in new projects in the areas of DFT, biomechanics, and high-performance scientific computing.

Education

Jun'15 - Ongoing

Ph.D. Candidate

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

Click here for a pdf of my CV


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.