Related papers: Fast Green Function Evaluation for Method of Momen…
In this work we develop a new algorithm for the efficient computation of the Voigt/complex error function. In particular, in this approach we propose a two-domain scheme where the number of the interpolation grid-points is dependent on the…
This article introduces new acceleration methods for fixed-point iterations. Extrapolations are computed using two or three mappings alternately and a new type of step length is proposed with good properties for nonlinear applications. The…
We propose an adaptive accelerated gradient method for solving smooth convex optimization problems. The method incorporates a scheme to determine the step size adaptively, by means of a local estimation of the smoothness constant, which is…
In this paper, we propose a novel approach to obtaining a reliable and simple mathematical model of a dielectrophoretic force for model-based feedback micromanipulation. Any such model is expected to sufficiently accurately relate the…
We consider the expansion of wave packets governed by the free Schr\"odinger equation. This seemingly simple task plays an important role in simulations of various quantum experiments and in particular in the field of matter-wave…
We propose a mesh refinement technique for solving elliptic difference equations on unbounded domains based on the fast lattice Green's function (FLGF) method. The FLGF method exploits the regularity of the Cartesian mesh and uses the fast…
We perform an extrapolative analysis of "fast-growth" free-energy-difference (DF) estimates of a computer-modeled, fully-solvated ethane<->methanol transformation. The results suggest that extrapolation can greatly reduce the systematic…
This study presents fast and accurate analytical methods for transient thermal modeling in multi-layer composites with an arbitrary number of layers. The proposed approach accounts for internal heat generation and non-homogeneities in the…
A new method is presented for solving Poisson's equation inside an open-ended rectangular pipe. The method uses Fast Fourier Transforms (FFTs) to perform mixed convolutions and correlations of the charge density with the Green function.…
The Green's function method is recognized to be a very powerful tool for modelling quantum transport in nanoscale electronic devices. As atomistic calculations are generally expensive, numerical methods and related algorithms have been…
We present a novel potential model for calculating the interaction between a molecule and a single graphene sheet. The dispersion/repulsion, induction, dipole-quadrupole, quadrupole-quadrupole interactions between a fluid molecule and a…
Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-form expression necessitates surrogate modeling to guide the…
In this paper it is shown how the generating functional for Green's functions in relativistic quantum field theory and in thermal field theory can be evaluated in terms of a standard quantum mechanical path integral. With this calculational…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
The feasibility of extrapolation of completely monotone functions can be quantified by examining the worst case scenario, whereby a pair of completely monotone functions agree on a given interval to a given relative precision, but differ as…
A classical problem in acoustic (and electromagnetic) scattering concerns the evaluation of the Green's function for the Helmholtz equation subject to impedance boundary conditions on a half-space. The two principal approaches used for…
We provide quantitative inductive estimates for Green's functions of matrices with (sub)expoentially decaying off diagonal entries in higher dimensions. Together with Cartan's estimates and discrepancy estimates, we establish explicit…
Evaluating the log-sum-exp function or the softmax function is a key step in many modern data science algorithms, notably in inference and classification. Because of the exponentials that these functions contain, the evaluation is prone to…
The approximate computation of all gravitational forces between $N$ interacting particles via the fast multipole method (FMM) can be made as accurate as direct summation, but requires less than $\mathcal{O}(N)$ operations. FMM groups…
The Empirical Interpolation Method (EIM) is a greedy procedure that constructs approximate representations of two-variable functions in separated form. In its classical presentation, the two variables play a non-symmetric role. In this…