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We present solutions to the Einstein-Klein Gordon system representing boson stars in the slow rotation approximation. By considering slow rotation we are able to reduce the number of equations yielding a system of ordinary differential…
We propose a deep learning framework based on an encoder-decoder architecture for the design and evaluation of cloaking devices, demonstrated in this work for two-dimensional wave propagation governed by the Helmholtz equation. The cloaks…
We present an explicit numerical scheme to solve the variable coefficient wave equation in one space dimension with minimal restrictions on the coefficient and initial data.
This article proposes spectral numerical methods to solve the time evolution of convection problems with viscosity strongly depending on temperature at infinite Prandtl number. Although we verify the proposed techniques just for viscosities…
Electromagnetic waves arise in many area of physics. Solutions are difficult to find in the general case. In this paper, we numerically integrate Maxwell equations in a 3D spherical polar coordinate system. Straightforward finite difference…
In this work we consider the method of non-linear boundary integral equation for solving numerically the inverse scattering problem of obliquely incident electromagnetic waves by a penetrable homogeneous cylinder in three dimensions. We…
We consider the hyperboloidal initial value problem in numerical relativity, motivated by the goal to evolve radiating compact objects such as black hole binaries with a numerical grid that includes null infinity. Unconstrained evolution…
We prove convergence of the spectral element method for piecewise polynomial collocation applied to periodic boundary value problems for functional differential equations. In particular, we prove that the numerical collocation solution…
The present work investigates the numerical evolution of linearized oscillations of non-rotating, spherically symmetric neutron stars within the framework of general relativity. We derive the appropriate equations using the (3+1)-formalism.…
We introduce a new numerical method for solving time-harmonic acoustic scattering problems. The main focus is on plane waves scattered by smoothly varying material inhomogeneities. The proposed method works for any frequency $\omega$, but…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
In the present paper we describe a simple black box algorithm for efficiently and accurately solving scattering problems related to the scattering of time-harmonic waves from radially-symmetric potentials in two dimensions. The method uses…
We propose an algorithm for rotational sparse coding along with an efficient implementation using steerability. Sparse coding (also called dictionary learning) is an important technique in image processing, useful in inverse problems,…
The process of a stationary range formation in the wind-wave spectrum is investigated numerically. The evolution equation for the two-dimensional wind-wave spectrum is numerically solved by using an exact calculation of the Hasselmann…
Existing methods for rotation estimation between two spherical ($\mathbb{S}^2$) patterns typically rely on spherical cross-correlation maximization between two spherical function. However, these approaches exhibit computational complexities…
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…
We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almost-banded infinite-dimensional systems. This…
We present an overarching framework for stable spectral methods on a triangle, defined by a multivariate W-system and based on orthogonal polynomials on the triangle. Motivated by the Koornwinder orthogonal polynomials on the triangle, we…
Non-axisymmetric oscillations of rapidly rotating relativistic stars are studied using the Cowling approximation. The oscillation spectra have been estimated by Fourier transforming the evolution equations describing the perturbations. This…
The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz…