Related papers: Computation of volume potentials over bounded doma…
The problem of determining the volume of a tubular neighbourhood has a long and rich history. Bounds on the volume of neighbourhoods of algebraic sets have turned out to play an important role in the probabilistic analysis of condition…
A high-order quadrature algorithm is presented for computing integrals over curved surfaces and volumes whose geometry is implicitly defined by the level sets of (one or more) multivariate polynomials. The algorithm recasts the implicitly…
An efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with Daubechies wavelet and scaling function basis sets. Our…
It is a widely held view that analytical integration is more accurate than the numerical one. In some special cases, however, numerical integration can be more advantageous than analytical integration. In our paper we show this benefit for…
We compute explicitly the Riemannian volume, with respect to the Fubini-Study metric, of a domain bounded by a Hermitian quadric in complex projective space. The volume is a rational function of the eigenvalues of the defining quadratic…
This paper introduces a novel method for the efficient and accurate computation of the volume of a domain whose boundary is given by an orientable hypersurface which is implicitly given as the iso-contour of a sufficiently smooth level-set…
We study numerical conformal mapping of multiply connected planar domains with boundaries consisting of unions of finitely many circular arcs, so called polycircular domains. We compute the conformal capacities of condensers defined by…
Future quantum computers may serve as a tool to access non-perturbative real-time correlation functions. In this talk, we discuss the prospects of using these to study Compton scattering for arbitrary kinematics. The restriction to a…
We study frequency domain electromagnetic scattering at a bounded, penetrable, and inhomogeneous obstacle $ \Omega \subset \mathbb{R}^3 $. From the Stratton-Chu integral representation, we derive a new representation formula when constant…
It is shown that quadrature formulas in many different applications can be derived from rational approximation of the Cauchy transform of a weight function. Since rational approximation is now a routine technology, this provides an easy new…
The purpose of this work is to introduce a strategy for determining the nodes and weights of a low-cardinality positive cubature formula nearly exact for polynomials of a given degree over spherical polygons. In the numerical section we…
In this paper the numerical solution of potential problems defined on 3D unbounded domains is addressed with Boundary Element Methods (BEMs), since in this way the problem is studied only on the boundary, and thus any finite approximation…
The approximate numerical method for a calculation of a quantum wave impedance in a case of a potential energy with a complicated spatial structure is considered. It was proved that the approximation of a real potential by a piesewise…
In this work we develop an approach to obtain analytical expressions for potentials in an impenetrable box. It is illustrated through the particular cases of the harmonic oscillator and the Coulomb potential. In this kind of system the…
Quantum computers hold promise to enable efficient simulations of the properties of molecules and materials; however, at present they only permit ab initio calculations of a few atoms, due to a limited number of qubits. In order to harness…
The 1/r Coulomb potential is calculated for a two dimensional system with periodic boundary conditions. Using polynomial splines in real space and a summation in reciprocal space we obtain numerically optimized potentials which allow us…
We propose an approach to compute inner and outer-approximations of the sets of values satisfying constraints expressed as arbitrarily quantified formulas. Such formulas arise for instance when specifying important problems in control such…
A mathematical proposition with a trainable pair, operator and quantum circuit, are introduced to approximate functions expressed as cubic Taylor polynomials, numerical simulations illustrate three cases.
Analytic relations are derived for finite volume integrals over the radial distribution function of a fluid, so-called Kirkwood-Buff integrals. Closed form expressions are obtained for cubes and cuboids, the system shapes commonly employed…
We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we…