Related papers: Numerical evolutions of fields on the 2-sphere usi…
This paper is concerned with the inverse scattering problem which aims to determine the spatially distributed dielectric constant coefficient of the 2D Helmholtz equation from multifrequency backscatter data associated with a single…
To solve the spinor-spinor Bethe-Salpeter equation in Euclidean space we propose a novel method related to the use of hyperspherical harmonics. We suggest an appropriate extension to form a new basis of spin-angular harmonics that is…
We develop an efficient numerical method for calculating the image stress field induced by spherical voids in materials. The method is applied to dislocation-void interactions in dislocation dynamics simulations. We obtain a complete set of…
We consider the 2D quasi-periodic scattering problem in optics, which has been modelled by a boundary value problem governed by Helmholtz equation with transparent boundary conditions. A spectral collocation method and a tensor product…
The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations…
Computation of the spherical harmonic rotation coefficients or elements of Wigner's d-matrix is important in a number of quantum mechanics and mathematical physics applications. Particularly, this is important for the Fast Multipole Methods…
We evaluate the performance of novel numerical methods for solving one-dimensional nonlinear fractional dispersive and dissipative evolution equations. The methods are based on affine combinations of time-splitting integrators and…
We demonstrate a fast spin-s spherical harmonic transform algorithm, which is flexible and exact for band-limited functions. In contrast to previous work, where spin transforms are computed independently, our algorithm permits the…
The time evolution of linear fields of spin $s = \pm 1$ and $s = \pm 2$ on Kerr black hole spacetimes are investigated by solving the homogeneous Teukolsky equation numerically. The applied numerical setup is based on a combination of…
We develop a numerical method for computing with orthogonal polynomials that are orthogonal on multiple, disjoint intervals for which analytical formulae are currently unknown. Our approach exploits the Fokas--Its--Kitaev Riemann--Hilbert…
A novel numerical approach to solving the shallow-water equations on the sphere using high-order numerical discretizations in both space and time is proposed. A space-time tensor formalism is used to express the equations of motion…
We propose a number of variational regularisation methods for the estimation and decomposition of motion fields on the $2$-sphere. While motion estimation is based on the optical flow equation, the presented decomposition models are…
We develop new adaptive algorithms for temporal integration of nonlinear evolution equations on tensor manifolds. These algorithms, which we call step-truncation methods, are based on performing one time step with a conventional…
We present a systematic numerical iteration approach to study the evolution properties of the spin-boson systems, which works well in whole coupling regime. This approach involves the evaluation of a set of coefficients for the formal…
To solve the spinor-spinor Bethe-Salpeter equation in Euclidean space we propose a novel method related to the use of hyperspherical harmonics. We suggest an appropriate extension to form a new basis of spin-angular harmonics that is…
A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, and…
In many applications data are measured or defined on a spherical manifold; spherical harmonic transforms are then required to access the frequency content of the data. We derive algorithms to perform forward and inverse spin spherical…
Recently there has been a growing interest in computational methods for quantum scattering equations that avoid the traditional decomposition of wave functions and scattering amplitudes into partial waves.The aim of the present work is to…
We review two numerical methods related to the Schramm-Loewner evolution (SLE). The first simulates SLE itself. More generally, it finds the curve in the half-plane that results from the Loewner equation for a given driving function. The…
Circle- and sphere-valued data play a significant role in inverse problems like magnetic resonance phase imaging and radar interferometry, in the analysis of directional information, and in color restoration tasks. In this paper, we aim to…