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A data-driven, model-free framework is introduced for calculating Reduced-Order Models (ROMs) capable of accurately predicting time-mean responses to external forcings, or forcings needed for specified responses, e.g., for control, in fully…
Time-dependent density functional theory (TDDFT) is a widely used method to investigate electron dynamics under various external perturbations such as laser fields. In this work, we present a novel approach to accelerate real time TDDFT…
A collision-based hybrid method for the discrete ordinates approximation of the multigroup neutron transport equation is developed for two-dimensional time-dependent problems. At each time step, this algorithm splits the neutron transport…
A revised and greatly improved version of the 3D continuum radiative transfer code MC3D is presented. It is based on the Monte-Carlo method and solves the radiative transfer problem self-consistently. It is designed for the simulation of…
We study numerical methods for dissipative particle dynamics (DPD), which is a system of stochastic differential equations and a popular stochastic momentum-conserving thermostat for simulating complex hydrodynamic behavior at mesoscales.…
Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for…
We present a wavefunction methodology to account for finite temperature initial conditions in the quantum Rabi model. The approach is based on the Davydov-Ansatz together with a statistical sampling of the canonical harmonic oscillator…
Dynamic mode decomposition (DMD), which the family of singular-value decompositions (SVD), is a popular tool of data-driven regression. While multiple numerical tests demonstrated the power and efficiency of DMD in representing data (i.e.,…
Absorption spectroscopy is traditionally used to determine the average gas temperature and species concentration along the laser line-of-sight by measuring the magnitude of two or more absorption transitions with different temperature…
In this work, we present a mixed precision algorithm that leverages the Gram matrix and Jacobi methods to compute the singular value decomposition (SVD) of tall-and-skinny matrices. By constructing the Gram matrix in higher precision and…
Tensor decomposition is an important tool for multiway data analysis. In practice, the data is often sparse yet associated with rich temporal information. Existing methods, however, often under-use the time information and ignore the…
The ability of widely distributed radar systems to capture diverse spatial scattering properties substantially improves radar imaging performance. Traditional imaging methods leverage regularized optimization techniques to reconstruct…
Low-rank methods have emerged as a promising strategy for reducing the memory footprint and computational cost of discrete-ordinates discretizations of the radiative transfer equation (RTE). However, most existing rank-adaptive approaches…
Solution interpolation between deforming meshes is an important component for several applications in scientific computing, including indirect arbitrary-Lagrangian-Eulerian and rezoning moving mesh methods in numerical solution of partial…
We describe two separate wavelength discretization schemes that can be used in the numerical solution of the comoving frame radiative transfer equation. We present an improved second order discretization scheme and show that it leads to…
Recently, there has been great interest in connections between continuous-time dynamical systems and optimization methods, notably in the context of accelerated methods for smooth and unconstrained problems. In this paper we extend this…
This paper considers the iterative solution of linear systems arising from discretization of the anisotropic radiative transfer equation with discontinuous elements on the sphere. In order to achieve robust convergence behavior in the…
We propose a nonperturbative scheme for the calculation of thermal damping-rates using exact renormalization group (RG)-equations. Special emphasis is put on the thermal RG where first results for the rate were given in M. Pietroni, Phys.…
A method for the fast and accurate solution of the radiative transfer equation in plane-parallel media with coherent isotropic scattering is presented. This largely analytical approach uses the formalism of meromorphic functions in order to…
Melting is a high temperature process that requires extensive sampling of configuration space, thus making melting temperature prediction computationally very expensive and challenging. Over the past few years, I have built two methods to…