Related papers: Function-Space Based Solution Scheme for the Size-…
We present an efficient numerical method, inspired by transformation optics, for solving the Poisson equation in complex and arbitrarily shaped geometries. The approach operates by mapping the physical domain to a uniform computational…
We study an exactly solvable quantum field theory (QFT) model describing interacting fermions in 2+1 dimensions. This model is motivated by physical arguments suggesting that it provides an effective description of spinless fermions on a…
We apply Density Functional Theory (DFT) and the DFT+U technique to study the adsorption of transition metal porphine molecules on atomistically flat Au(111) surfaces. DFT calculations using the Perdew-Burke-Ernzerhof (PBE) exchange…
The Dynamical Mean Field Theory (DMFT) is a powerful tool for calculating highly correlated systems (both bosonic and fermionic) in a state of thermodynamic equilibrium. However, in the case of non-equilibrium states, the method has…
The preconditioned Crank-Nicolson (pCN) method is a Markov Chain Monte Carlo (MCMC) scheme, specifically designed to perform Bayesian inferences in function spaces. Unlike many standard MCMC algorithms, the pCN method can preserve the…
This review discusses progress in efficient solvers which have as their foundation a representation in real space, either through finite-difference or finite-element formulations. The relationship of real-space approaches to linear-scaling…
Over the last two decades, several fast, robust, and high-order accurate methods have been developed for solving the Poisson equation in complicated geometry using potential theory. In this approach, rather than discretizing the partial…
An efficient surface integral equation-based method is proposed for the analysis of electromagnetic scattering from multilayered media containing complex periodic inclusions. The proposed method defines equivalent currents at the interfaces…
In this work we perform a Green's function analysis of giant-dipole systems. First we derive the Green's functions of different magnetically field-dressed systems, in particular of electronically highly excited atomic species in crossed…
The evolution of fifth generation (5G) wireless communication networks has led to an increased need for wireless resource management solutions that provide higher data rates, wide coverage, low latency, and power efficiency. Yet, many of…
The standard Dynamic Programming (DP) formulation can be used to solve Multi-Stage Optimization Problems (MSOP's) with additively separable objective functions. In this paper we consider a larger class of MSOP's with monotonically backward…
Bayesian Physics Informed Neural Networks (BPINN) have attracted considerable attention for inferring the system states and physical parameters of differential equations according to noisy observations. However, in practice, Hamiltonian…
For many chemical processes the accurate description of solvent effects are vitally important. Here, we describe a hybrid ansatz for the explicit quantum mechanical description of solute-solvent and solvent-solvent interactions based on…
We construct a new functional for the single particle Green's function, which is a variant of the standard Baym Kadanoff functional. The stability of the stationary solutions to the new functional is directly related to aspects of the…
We revisit the image charge method for the Green's function problem of the Poisson-Boltzmann equation for a dielectric sphere immersed in ionic solutions. Using finite Mellin transformation, we represent the reaction potential due to a…
We implement an efficient numerical method to calculate response functions of complex impurities based on the Density Matrix Renormalization Group (DMRG) and use it as the impurity-solver of the Dynamical Mean Field Theory (DMFT). This…
This work proposes a fast iterative method for local steric Poisson--Boltzmann (PB) theories, in which the electrostatic potential is governed by the Poisson's equation and ionic concentrations satisfy equilibrium conditions. To present the…
We develop a static quantum embedding scheme that utilizes different levels of approximations to coupled cluster (CC) theory for an active fragment region and its environment. To reduce the computational cost, we solve the local fragment…
In this paper, we present a fast multipole method (FMM) for the half-space Green's function in a homogeneous elastic half-space subject to zero normal stress, for which an explicit solution was given by Mindlin (1936). The image structure…
We explore the use of exact diagonalization methods for solving the self consistent equations of the cellular dynamical mean field theory (CDMFT) for the one dimensional regular and extended Hubbard models. We investigate the nature of the…