Related papers: Numerical evolutions of fields on the 2-sphere usi…
In this paper, we describe a numerical method to solve numerically the weakly dispersive fully nonlinear Serre-Green-Naghdi (SGN) celebrated model. Namely, our scheme is based on reliable finite volume methods, proven to be very effective…
Inverse scattering involving microwave and ultrasound waves require numerical solution of nonlinear optimization problem. To alleviate the computational burden of a full three-dimensional (3-D) inverse problem, it is a common practice to…
We report on the successful numerical evolution of the compactified hyperboloidal initial value problem in general relativity using generalized harmonic gauge. We work in spherical symmetry, using a massless scalar field to drive dynamics.…
A variety of inverse Sturm-Liouville problems is considered, including the two-spectrum inverse problem, the problem of recovering the potential from the Weyl function, as well as the recovery from the spectral function. In all cases the…
We solve the shifted wave equation \begin{align*} \frac{\partial^2}{\partial t^2}\varphi(x,t)=(\Delta_x+\rho^2)\varphi(x,t) \end{align*} on a non compact simply connected harmonic manifold with mean curvature of the horospheres $2\rho>0$.…
We focus on an alignment-free method to estimate the underlying signal from a large number of noisy randomly shifted observations. Specifically, we estimate the mean, power spectrum, and bispectrum of the signal from the observations. Since…
Numerical homogenization tries to approximate the solutions of elliptic partial differential equations with strongly oscillating coefficients by functions from modified finite element spaces. We present in this paper a class of such methods…
Differential equations may possess coefficients that vary on a spectrum of scales. Because coefficients are typically multiplicative in real space, they turn into convolution operators in spectral space, mixing all wavenumbers. However, in…
We present new results building on the conservative deterministic spectral method for the space inhomogeneous Boltzmann equation developed by Gamba and Tharkabhushaman. This approach is a two-step process that acts on the weak form of the…
This paper addresses the electromagnetic inverse scattering problem of determining the location and shape of anisotropic objects from near-field data. We investigate both cases involving the Helmholtz equation and Maxwell's equations for…
This article is concerned with the derivation of numerical reconstruction schemes for the inverse moving source problem on determining source profiles in (time-fractional) evolution equations. As a continuation of the theoretical result on…
The mathematical representations of data in the Spherical Harmonic (SH) domain has recently regained increasing interest in the machine learning community. This technical report gives an in-depth introduction to the theoretical foundation…
We propose an algorithm for robust recovery of the spherical harmonic expansion of functions defined on the d-dimensional unit sphere $\mathbb{S}^{d-1}$ using a near-optimal number of function evaluations. We show that for any $f \in…
The use of spectral projection based methods for simulation of a stochastic system with discontinuous solution exhibits the Gibbs phenomenon, which is characterized by oscillations near discontinuities. This paper investigates a dynamic…
Recent microscopy imaging techniques allow to precisely analyze cell morphology in 3D image data. To process the vast amount of image data generated by current digitized imaging techniques, automated approaches are demanded more than ever.…
We introduce a nonstationary spatio-temporal statistical model for gridded data on the sphere. The model specifies a computationally convenient covariance structure that depends on heterogeneous geography. Widely used statistical models on…
This paper examines the temporal evolution of a two-stage stochastic model for spherical random fields. The model uses a time-fractional stochastic hyperbolic diffusion equation, which describes the evolution of spherical random fields on…
Two-dimensional (2D) vibrational spectroscopy is a powerful means of investigating the structure and dynamics of complex molecules in condensed phases. However, even in theory, analysis of 2D spectra resulting from complex inter- and…
In this paper, we design and analyze a novel spectral method for the subdiffusion equation. As it has been known, the solutions of this equation are usually singular near the initial time. Consequently, direct application of the traditional…
We compare two different numerical methods to integrate in time spatially delocalized initial densities using the Schr\"odinger-Poisson equation system as the evolution law. The basic equation is a nonlinear Schr\"odinger equation with an…