Ph.D. Student · Virginia Tech, Dept. of Mathematics

Amit
Rotem.

Numerical methods for partial differential equations and high-performance computing. Building scalable solvers for wave propagation and beyond.

Amit Rotem

About

Background

I am a Ph.D. student in the Department of Mathematics at Virginia Tech, advised by Daniel Appelö. My research focuses on numerical methods for partial differential equations (PDEs) with an emphasis on high-performance computing (HPC). My work lies at the intersection of algorithmic theory and scalable implementation. A central focus of my research is the development of the WaveHoltz method for solving frequency-domain wave propagation problems. This includes a general theory establishing convergence in the semi-discrete and fully discrete settings, alongside the design of computational strategies that are efficient on modern parallel architectures.

I earned both my B.S. and M.S. in Applied Mathematics and Statistics from the Colorado School of Mines. During that time, I worked on a project using machine learning to enhance the value of hyperspectral data in geosciences, bridging lab-based and field data collection techniques. As a graduate student, I have contributed to the MFEM finite element library, where I implemented a matrix-free interior penalty DG diffusion operator optimized for multi-GPU computing. In addition to my research at Virginia Tech, I collaborate with researchers at Lawrence Livermore National Laboratory on the GenDiL (Generic Discretization Library) project, which focuses on flexible, high-performance implementations of finite element methods in arbitrary dimensions.

Outside of research, I enjoy running, hiking, and traveling—not just to conferences. I’m an avid reader of fantasy novels and a fan of horror movies.

01 / Research

Interests & Ongoing Work

Numerical PDEs

Finite element and finite difference methods, the WaveHoltz iteration for frequency-domain wave propagation, and domain decomposition methods.

High Performance Computing

GPU and many-core distributed algorithms and implementations in C++. Matrix-free methods optimized for modern massively parallel hardware.

Ongoing Projects

02 / Publications

Research Papers

WaveHoltz waveguide simulation
01

Convergence of the Semi-Discrete WaveHoltz Iteration

Amit Rotem, Olof Runborg, Daniel Appelö

Journal of Computational Physics

Nematic liquid crystal simulation
02

A Domain Decomposition Approach to Accelerate Simulations of Structure Preserving Nematic Liquid Crystal Models

Sylver Carter, Amit Rotem, Shawn W Walker

Hyperspectral data visualization
03

Interpretation of Hyperspectral Shortwave Infrared Core Scanning Data Using SEM-Based Automated Mineralogy: a Machine Learning Approach

Amit Rotem, Alexander Vidal, Katharina Pfaff, Luis Tenorio, Matthias Chung, Erik Tharalson, Thomas Monecke

03 / Software

Projects & Contributions