Ph.D. Student · Virginia Tech, Dept. of Mathematics
Numerical methods for partial differential equations and high-performance computing. Building scalable solvers for wave propagation and beyond.
About
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
Finite element and finite difference methods, the WaveHoltz iteration for frequency-domain wave propagation, and domain decomposition methods.
GPU and many-core distributed algorithms and implementations in C++. Matrix-free methods optimized for modern massively parallel hardware.
02 / Publications
03 / Software
Domain decomposition solver for the Helmholtz equation in two and three dimensions implemented in CUDA.
Header-only C++ library providing flexible and efficient PDE discretization tools through a generic programming approach. High-performance FEM in arbitrary dimensions.
Modular parallel C++ library for finite element methods, enabling high-performance scalable FEM research and application development across laptop to supercomputer.
Discontinuous Galerkin implementation of the acoustic wave equation and other hyperbolic conservation laws.
Single-header C++ template library for structuring contiguous arrays into compile-time ranked tensor objects, similar to NumPy's ndarray.
A collection of numerical methods ranging from nonlinear optimization and ODE solvers to neural networks. Written as a personal undergraduate project.