Related papers: A splitting scheme for the quantum Liouville-BGK e…
We study a number of filtering schemes for the reduction of the statistical error in non-adiabatic calculations by means of the quantum-classical Liouville equation. In particular, we focus on a scheme based on setting a threshold value on…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
In this paper, we develop a class of high order conservative semi-Lagrangian (SL) discontinuous Galerkin (DG) methods for solving multi-dimensional linear transport equations. The methods rely on a characteristic Galerkin weak formulation,…
We study parameter estimation for the transport coefficients of the quark-gluon plasma by differentiating open-quantum-system-based Monte Carlo simulations of quarkonium suppression. The underlying simulator requires solving a Lindblad…
We present a quantum-assisted generative algorithm for synthetic tracks of Lagrangian tracer particles in a turbulent shear flow. The parallelism and sampling properties of quantum algorithms are used to build and optimize a parametric…
This paper addresses the challenge of scaling quantum computing by employing distributed quantum algorithms across multiple processors. We propose a novel circuit partitioning method that leverages graph partitioning to optimize both qubit…
The present article focuses on studying the extent to which the nonuniqueness that is inherent in the standard quantum mechanical calculation of arrival/transit time distribution can be exploited to enable an empirical scrutiny of any…
We study the Landau-de Gennes Q-tensor model of liquid crystals subjected to an electric field and develop a fully discrete numerical scheme for its solution. The scheme uses a convex splitting of the bulk potential, and we introduce a…
Fractional Fokker-Planck equation plays an important role in describing anomalous dynamics. To the best of our knowledge, the existing discussions mainly focus on this kind of equation involving one diffusion operator. In this paper, we…
This work introduces and rigorously analyzes a novel operator-splitting finite element scheme for approximating viscosity solutions of a broad class of constrained second-order partial differential equations. By decoupling the primary PDE…
Simulations of the discrete Boltzmann Bhatnagar-Gross-Krook (BGK) equation are an important tool for understanding fluid dynamics in non-continuum regimes. Here, we introduce a discontinuous Galerkin finite element method (DG-FEM) for…
Combining the classical theory of optimal transport with modern operator splitting techniques, we develop a new numerical method for nonlinear, nonlocal partial differential equations, arising in models of porous media, materials science,…
We introduce a fractional Klein-Kramers equation which describes sub-ballistic superdiffusion in phase space in the presence of a space-dependent external force field. This equation defines the differential L{\'e}vy walk model whose…
Semi-Lagrangian (SL) schemes are known as a major numerical tool for solving transport equations with many advantages and have been widely deployed in the fields of computational fluid dynamics, plasma physics modeling, numerical weather…
We develop a general framework for designing conservative numerical methods based on summation by parts operators and split forms in space, combined with relaxation Runge-Kutta methods in time. We apply this framework to create new classes…
In this work, we develop a localized numerical scheme with low regularity requirements for solving time-fractional integro-differential equations. First, a fully discrete numerical scheme is constructed. Specifically, for temporal…
A conservative discontinuous Galerkin scheme for a nonlinear Dougherty collision operator in full-f long-wavelength gyrokinetics is presented. Analytically this model operator has the advective-diffusive form of Fokker-Planck operators, it…
We study solution techniques for parabolic equations with fractional diffusion and Caputo fractional time derivative, the latter being discretized and analyzed in a general Hilbert space setting. The spatial fractional diffusion is realized…
We present GPUQT, a quantum transport code fully implemented on graphics processing units. Using this code, one can obtain intrinsic electronic transport properties of large systems described by a real-space tight-binding Hamiltonian…
We introduce a persistent random walk model for the stochastic transport of particles involving self-reinforcement and a rest state with Mittag-Leffler distributed residence times. The model involves a system of hyperbolic partial…