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.
I completed my high school from Kids Corner Senior Secondary School, Firozabad in May 2008.
This is a list of several of my projects over the last couple years!
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.
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.
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.
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).
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.
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.
Nov'17 - Dec'17 Independent Project
Implemented Discontinuous Galerkin Finite element method to solve a steady-state advection equation.
Apr'18 - Aug'18 Independent Project
Implemented Local Discontinuous Galerkin (LDG) Method to solve an unsteady convection-diffusion equation.
Jan'18 - Mar'18 Independent Project
Learned and Implemented Isogeometric Analysis to solve Laplace equation in a 2d domain.
Oct'17 Independent Project
Employed Automatic Differentiation (Sacado) to solve a non-linear minimal surface equation.
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.