Related papers: Continuous-stage symplectic adapted exponential me…
Recently, our group developed explicit symplectic methods for curved spacetimes that are not split into several explicitly integrable parts, but are via appropriate time transformations. Such time-transformed explicit symplectic integrators…
Constrained density functional theory (cDFT) is a versatile electronic structure method that enables ground-state calculations to be performed subject to physical constraints. It thereby broadens their applicability and utility. Automated…
Outstanding advances in solid-state laser technology, employing the optical parametric chirped-pulse-amplification (OPCPA) technique, have led physicists to focus laser pulses to highly-relativistic intensities which led to novel schemes…
In this article, we introduce a kind of numerical schemes, based on Pad$\acute{e}$ approximation, for two stochastic Hamiltonian systems which are treated separately. For the linear stochastic Hamiltonian systems, it is shown that the…
This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of…
The state of art of charge-conserving electromagnetic finite element particle-in-cell has grown by leaps and bounds in the past few years. These advances have primarily been achieved for leap-frog time stepping schemes for Maxwell solvers,…
This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane-mediated receptor dynamics on cell surfaces, we…
In this contribution, we present a numerical analysis of the continuous stochastic gradient (CSG) method, including applications from topology optimization and convergence rates. In contrast to standard stochastic gradient optimization…
We present a data-driven reduced-order modeling of the space-charge dynamics for electromagnetic particle-in-cell (EMPIC) plasma simulations based on dynamic mode decomposition (DMD). The dynamics of the charged particles in kinetic plasma…
We propose efficient numerical methods for nonseparable non-canonical Hamiltonian systems which are explicit, K-symplectic in the extended phase space with long time energy conservation properties. They are based on extending the original…
Many force-gradient explicit symplectic integration algorithms have been designed for the Hamiltonian $H=T (\mathbf{p})+V(\mathbf{q})$ with kinetic energy $T(\mathbf{p})=\mathbf{p}^2/2$ in the existing references. When the force-gradient…
An implementation of the coupled-cluster single- and double excitations (CCSD) method on two-dimensional quantum dots is presented. Advantages and limitations are studied through comparison with other high accuracy approaches for two to…
This work proposes and analyzes a generalized acceleration technique for decreasing the computational complexity of using stochastic collocation (SC) methods to solve partial differential equations (PDEs) with random input data. The SC…
A parallel implementation of coupled spin-lattice dynamics in the LAMMPS molecular dynamics package is presented. The equations of motion for both spin only and coupled spin-lattice dynamics are first reviewed, including a detailed account…
A basic leapfrog integrator and its energy-preserving and variational / symplectic variants are proposed and studied for the numerical integration of the equations of motion of relativistic charged particles in an electromagnetic field. The…
This letter studies symmetric and symplectic exponential integrators when applied to numerically computing nonlinear Hamiltonian systems. We first establish the symmetry and symplecticity conditions of exponential integrators and then show…
The state-of-the-art methods for solving optimization problems in big dimensions are variants of randomized coordinate descent (RCD). In this paper we introduce a fundamentally new type of acceleration strategy for RCD based on the…
Understanding the system-level spectral immittance response of capacitive energy storage devices with analytically tractable physics-based models is not only important for the progress of the technology, but also allows to develop new…
Quantum--Mechanical methods that are both computationally fast and accurate are not yet available for electronic excitations having charge transfer character. In this work, we present a significant step forward towards this goal for those…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…