Related papers: Simulating Maxwell-Schr\"odinger Equations by High…
We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we…
While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
We proposed a provably stable FDTD subgridding method for accurate and efficient transient electromagnetic analysis. In the proposed method, several field components are properly added to the boundaries of Yee's grid to make sure that the…
The finite-difference time-domain (FDTD) method, which is important in photonic hardware design flow, is widely adopted to solve time-domain Maxwell equations. However, FDTD is known for its prohibitive runtime cost, taking minutes to hours…
We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level…
To enhance the scalability and performance of the traditional finite-difference time-domain (FDTD) methods, a three-dimensional summation-by-parts simultaneous approximation term (SBP-SAT) FDTD method is developed to solve complex…
We propose a high-order FDTD scheme based on the correction function method (CFM) to treat interfaces with complex geometry without increasing the complexity of the numerical approach for constant coefficients. Correction functions are…
The simulation of nuclear magnetic resonance (NMR) experiments is a notoriously difficult task, if many spins participate in the dynamics. The recently established dynamic mean-field theory for high-temperature spin systems (spinDMFT)…
We take into account the dynamics of three types of models of rotating galaxies in polar coordinates in a rotating frame. Due to non-axisymmetric potential perturbations, the angular momentum varies with time, and the kinetic energy depends…
We show that a recently discovered fourth order symplectic algorithm, which requires one evaluation of force gradient in addition to three evaluations of the force, when iterated to higher order, yielded algorithms that are far superior to…
In this paper, we develop sixth-order hybrid finite difference methods (FDMs) for the elliptic interface problem $-\nabla \cdot( a\nabla u)=f$ in $\Omega\backslash \Gamma$, where $\Gamma$ is a smooth interface inside $\Omega$. The variable…
The most popular methods for self-consistent simulation of fields interacting with charged species is using finite difference time domain (FDTD) methods together with Newton's laws of motion to evolve locations and velocities of particles.…
We propose a novel Hermite-Taylor correction function method to handle embedded boundary and interface conditions for Maxwell's equations. The Hermite-Taylor method evolves the electromagnetic fields and their derivatives through order $m$…
We consider the variational discretization of a linear-quadratic optimal control problem with pointwise control and state constraints. In order to allow for a Fr\'echet smooth norm, the problem is reformulated by means of a reflexive…
Control of quantum systems via lasers has numerous applications that require fast and accurate numerical solution of the Schr\"odinger equation. In this paper we present three strategies for extending any sixth-order scheme for…
In this paper, we discuss the steady and time-dependent nonlinear convection-diffusion (advection-diffusion) equations with the Dirichlet boundary condition. For the steady nonlinear equation, we use an iteration method to reformulate the…
This paper devotes to combine the chirp basis function transformation and symplectic coordinates transformation to yield a novel Wigner distribution (WD) associated with the linear canonical transform (LCT), named as the symplectic WD in…
A new algorithm for efficient and fully time-reversible integration of first-principles molecular dynamics based on orbital-free density functional theory (OFDFT) is presented. The algorithm adapts to this nontrivial case the recently…
Numerical simulations of merging compact objects and their remnants form the theoretical foundation for gravitational wave and multi-messenger astronomy. While Cartesian-coordinate-based adaptive mesh refinement is commonly used for…