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We present the formulation, algorithm and numerical tests of the magnetohydrodynamic-particle-in-cell (MHD-PIC) method with particles treated under the guiding center approximation, which we term the MHD-gPIC method, and it is implemented…
This article presents stability and convergence analyses of subgrid multiscale stabilized finite element formulation of non-Newtonian power-law fluid flow model strongly coupled with variable coefficients Advection-Diffusion-Reaction…
The reliability of atomistic simulations depends on the quality of the underlying energy models providing the source of physical information, for instance for the calculation of migration barriers in atomistic Kinetic Monte Carlo…
We present a new pseudospectral algorithm for the calculation of the structure of atoms in strong magnetic fields. We have verified this technique for one, two and three-electron atoms in zero magnetic fields against laboratory results and…
The design and operation of modern energy systems are heavily influenced by time-dependent and uncertain parameters, e.g., renewable electricity generation, load-demand, and electricity prices. These are typically represented by a set of…
This paper presents a p-adaptive high-order hybridizable discontinuous Galerkin spectral element method (HDG-SEM) for solving the Poisson equation in electrostatic plasma simulations using particle-in-cell (PIC) schemes. This approach…
We theoretically propose a multidimensional high-harmonic echo spectroscopy technique which utilizes strong optical fields to resolve coherent electron dynamics spanning an energy range of multiple electron Volts. Using our recently…
In this dissertation, I introduce the principles and methods of effective field theory and describe my work in three EFTs: First, in the perturbative QCD region, I use soft collinear effective theory (SCET) to prove that strong interaction…
Molecular dynamics (MD) simulation is essential for various scientific domains but computationally expensive. Learning-based force fields have made significant progress in accelerating ab-initio MD simulation but are not fast enough for…
Upcoming Large Scale Structure surveys aim to achieve an unprecedented level of precision in measuring galaxy clustering. However, accurately modeling these statistics may require theoretical templates that go beyond second-order…
With the proliferation of smart grids, smart cities face growing challenges due to cyber-attacks and sophisticated electricity theft behaviors, particularly in residential photovoltaic (PV) generation systems. Traditional Electricity Theft…
The exact numerical simulation of plasma turbulence is one of the assets and challenges in fusion research. For grid-based solvers, sufficiently fine resolutions are often unattainable due to the curse of dimensionality. The sparse grid…
We present a fully grid-based approach for solving Hartree-Fock and all-electron Kohn-Sham equations based on low-rank approximation of three-dimensional electron orbitals. Due to the low-rank structure the total complexity of the algorithm…
We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. We interchangeably use particle and grid representations of transported quantities to balance efficiency and accuracy. A novel…
We study the geometric particle-in-cell methods for an electrostatic hybrid plasma model. In this model, ions are described by the fully kinetic equations, electron density is determined by the Boltzmann relation, and space-charge effects…
We present a general method for incorporating the electromagnetic interaction into descriptions of hadronic processes based on four-dimensional scattering integral equations. The method involves the idea of gauging the scattering equations…
We present the numerical implementation of the time-dependent complete-active-space self-consistent-field (TD-CASSCF) method [Phys. Rev. A, 88, 023402 (2013)] for atoms driven by a strong linearly polarized laser pulse. The present…
We develop a first-principles simulation method for attosecond time-resolved photoelectron spectroscopy. This method enables us to directly simulate the whole experimental processes, including excitation, emission and detection on equal…
We present a variational augmentation procedure to optimize the exponents of Gaussian continuum basis sets for simulating strong-field laser ionization phenomena such as higher harmonic generation (HHG) in atoms and ions using the…
We developed a general framework for hybrid quantum-classical computing of molecular and periodic embedding approaches based on an orbital space separation of the fragment and environment degrees of freedom. We demonstrate its potential by…