Related papers: Solving Vlasov-Poisson system with an adaptive Her…
We describe a new, adaptive solver for the two-dimensional Poisson equation in complicated geometries. Using classical potential theory, we represent the solution as the sum of a volume potential and a double layer potential. Rather than…
A new lattice Boltzmann scheme associated with flexible specific heat ratio is proposed. The new free degree is introduced via the internal energy associated with the internal structure. The evolution equation of the distribution function…
This paper introduces a new approximation scheme for solving high-dimensional semilinear partial differential equations (PDEs) and backward stochastic differential equations (BSDEs). First, we decompose a target semilinear PDE (BSDE) into…
In this paper, we consider a class of highly oscillatory Hamiltonian systems which involve a scaling parameter $\varepsilon\in(0,1]$. The problem arises from many physical models in some limit parameter regime or from some time-compressed…
The manuscript presents a new technique for computing the exponential of skew-Hermitian operators. Principal advantages of the proposed method include: stability even for large time-steps, the possibility to parallelize in time over many…
This paper proposes several explicit and implicit multistep frequency response optimized integrators considering first or second order derivative. A prediction-based method aiming at accelerating a novel power system transient simulation…
This paper presents an efficient parallel direct algorithm with near-optimal complexity for the compact fourth and sixth-order approximation of the three-dimensional Helmholtz equations [1] with the problem coefficient depending on only one…
We design a variational asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck system with the high field scaling, which describes the Brownian motion of a large system of particles in a surrounding bath. Our scheme builds on an…
Penalized estimation methods for diffusion processes and dependent data have recently gained significant attention due to their effectiveness in handling high-dimensional stochastic systems. In this work, we introduce an adaptive…
This research focuses on solving time-dependent partial differential equations (PDEs), in particular the time-dependent Schr\"odinger equation, using matrix product states (MPS). We propose an extension of Hermite Distributed Approximating…
Accurate prediction of the frequency response of quantum dots under electromagnetic radiation is essential for investigating absorption spectra, excitonic effects, and nonlinear optical behavior in quantum dots and semiconductor…
The need for fast sparse optimization is emerging, e.g., to deal with large-dimensional data-driven problems and to track time-varying systems. In the framework of linear sparse optimization, the iterative shrinkage-thresholding algorithm…
This work extends our previous study from S. Shrestha et al. (2024) by introducing a new abstract framework for Variational Multiscale (VMS) methods at the discrete level. We introduce the concept of what we define as the optimal projector…
Using Hermite's formulation of polynomial stability conditions, static output feedback (SOF) controller design can be formulated as a polynomial matrix inequality (PMI), a (generally nonconvex) nonlinear semidefinite programming problem…
We study the nonparametric estimation of the jump density of a compound Poisson process from the discrete observation of one trajectory over $[0,T]$. We consider the microscopic regime when the sampling rate $\Delta=\Delta_T\rightarrow0$ as…
We propose a new splitting method for strong numerical solution of the Cox-Ingersoll-Ross model. For this method, applied over both deterministic and adaptive random meshes, we prove a uniform moment bound and strong error results of order…
We present a new primitive for quantum algorithms that implements a discrete Hermite transform efficiently, in time that depends logarithmically in both the dimension and the inverse of the allowable error. This transform, which maps basis…
We present a revision to the well known Stormer-Verlet algorithm for simulating second order differential equations. The revision addresses the inclusion of linear friction with associated stochastic noise, and we analytically demonstrate…
The desire for wide-field of view, large fractional bandwidth, high sensitivity, high spectral and temporal resolution has driven radio interferometry to the point of big data revolution where the data is represented in at least three…
The Vlasov equation is a nonlinear partial differential equation that provides a first-principles description of the dynamics of plasmas. Its linear limit is routinely used in plasma physics to investigate plasma oscillations and stability.…