Related papers: Hybrid Basis Scheme for computing Electrostatic fi…
This paper is devoted to the numerical symplectic approximation of the charged-particle dynamics (CPD) with arbitrary electromagnetic fields. By utilizing continuous-stage methods and exponential integrators, a general class of symplectic…
Using techniques from geometry and complex analysis in their simplest form, we present a derivation of electric fields on surfaces with non-trivial topology. A byproduct of this analysis is an intuitive visualization of elliptic functions…
We describe an efficient numerical method for simulating the dynamics of interacting spin ensembles in the presence of dephasing and decay. The method builds on the discrete truncated Wigner approximation for isolated systems, which…
The fluid structure interaction of cylinders in tandem arrangement is used as validation basis of a multi-domain Lagrangian-Eulerian hybrid flow solver. In this hybrid combination, separate grids of limited width are defined around every…
An improved unified formulation based on the effective field theory is introduced for a spin-1/2 Ising model with nearest neighbor interactions with arbitrary coordination number z. Present formulation is capable of calculating all the…
Magnetically-sensitive experiments and newly-developed quantum technologies with integrated high-permeability magnetic shields require increasing control of their magnetic field environment and reductions in size, weight, power and cost.…
This paper presents a re-formulation of the boundary integral method (BIM) for the Debye-Huckel model of molecular and colloidal electrostatics that removes the mathematical singularities that have been accepted as an intrinsic part of the…
In the absence of wave propagation, transient electromagnetic fields are governed by a composite scalar/vector potential formulation for the quasistatic Darwin field model. Darwin-type field models are capable of capturing inductive,…
We present an approach to solid-state electronic-structure calculations based on the finite-element method. In this method, the basis functions are strictly local, piecewise polynomials. Because the basis is composed of polynomials, the…
To overcome the limitations of existing algorithms for solving self-bound quantum many-body problems -- such as those encountered in nuclear and particle physics -- that access only a restricted subset of energy levels and provide limited…
Phase field methods have been widely used to study phase transitions and polarization switching in ferroelectric thin films. In this paper, we develop an efficient numerical scheme for the variational phase field model based on variational…
We introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation of the problem and the concepts of the domain decomposition…
A numerical method is presented for first-principle simulations of charged colloidal dispersions in electrolyte solutions. Utilizing a smoothed profile for colloid-solvent boundaries, efficient mesoscopic simulations are enabled for…
The increasing prevalence of neural networks in safety-critical control systems underscores the imperative need for rigorous methods to ensure the reliability and safety of these systems. This work introduces a novel approach employing…
We address in this work the question of the discretization of two-dimensional periodic Dirac Hamiltonians. Standard finite differences methods on rectangular grids are plagued with the so-called Fermion doubling problem, which creates…
We present the N-body simulation techniques in EXP. EXP uses empirically-chosen basis functions to expand the potential field of an ensemble of particles. Unlike other basis function expansions, the derived basis functions are adapted to an…
We introduce a new basis function (the spherical gaussian) for electronic structure calculations on spheres of any dimension $D$. We find \alert{general} expressions for the one- and two-electron integrals and propose an efficient…
We present a new multilevel method for calculating Poisson's equation, which often arises form electrostatic problems, by using hierarchical loop bases. This method, termed hierarchical Loop basis Poisson Solver (hieLPS), extends previous…
Analyzing electromagnetic fields in complex, multi-material environments presents substantial computational challenges. To address these, we propose a hybrid numerical method that couples discrete exterior calculus (DEC) with surface…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…