Related papers: Generalized Sturmian Functions in prolate spheroid…
Distributed order fractional operators offer a rigorous tool for mathematical modelling of multi-physics phenomena, where the differential orders are distributed over a range of values rather than being just a fixed integer/fraction as it…
Complex processes in perforated domains occur in many real-world applications. These problems are typically characterized by physical processes in domains with multiple scales (see Figure 1 for the illustration of a perforated domain).…
An accelerated boundary integral method for Stokes flow of a suspension of deformable particles is presented for an arbitrary domain and implemented for the important case of a planar slit geometry. The computational complexity of the…
In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A function that has a prescribed value on the domain in which a differential…
In his monograph Chebyshev and Fourier Spectral Methods, John Boyd claimed that, regarding Fourier spectral methods for solving differential equations, ``[t]he virtues of the Fast Fourier Transform will continue to improve as the relentless…
Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The…
An algorithm for the calculation of hyperfine structure and spectra of diatomic molecules based on the variational nuclear motion is presented. Hyperfine coupling terms considered are Fermi-contact, nuclear spin-electron spin dipole-dipole,…
We develop a fast method for computing the electrostatic energy and forces for a collection of charges in doubly-periodic slabs with jumps in the dielectric permittivity at the slab boundaries. Our method achieves spectral accuracy by using…
The spectral form factor (SFF) plays a crucial role in revealing the statistical properties of energy level distributions in complex systems. It is one of the tools to diagnose quantum chaos and unravel the universal dynamics therein. The…
The paper focuses on numerical solution of parametrized diffusion equations with scalar parameter-dependent coefficient function by the stochastic (spectral) Galerkin method. We study preconditioning of the related discretized problems…
In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A continuous function, the domain parameter, is used to modify the original…
Static electric response properties of atoms and molecules are reported within the real-space Cartesian grid implementation of pseudopotential Kohn-Sham (KS) density functional theory (DFT). A detailed systematic investigation is made for a…
This paper describes the implementation of the direct solution method (DSM) using radial spectral elements for the calculation of synthetic seismograms in self-gravitating, spherically symmetric, non-rotating, anelastic, and transversely…
A finite difference scheme is used to develop a numerical method to solve the flow of an unbounded viscoelastic fluid with zero to moderate inertia around a prolate spheroidal particle. The equations are written in prolate spheroidal…
This article provides a general iterative approximation to partial differential equations, and thus establish existence of smooth solution. The heart of the method is to contract (or expand) the boundary conditions uniformly in the domain,…
We developed a general framework for hybrid quantum-classical computing of molecular and periodic embedding approaches based on an orbital space separation of the fragment and environment degrees of freedom. We demonstrate its potential by…
We present a refinement of the Spectral Method by incorporating an optimization method into it and generalize it to two space dimensions. We then apply this Refined Spectral Method as an extremely accurate technique for finding the bound…
We present a fast algorithm to calculate Coulomb/exchange integrals of prolate spheroidal electronic orbitals, which are the exact solutions of the single-electron, two-center Schr\"odinger equation for diatomic molecules. Our approach…
Density functional theory (DFT) has emerged as one of the most versatile and lucrative approaches in electronic structure calculations of many-electron systems in past four decades. Here we give an account of the development of a…
Single-particle resonances are crucial for exotic nuclei near and beyond the drip lines. Since the majority of nuclei are deformed, the interplay between deformation and orbital structure near threshold becomes very important and can lead…