Related papers: Highly efficient Gauss's law-preserving spectral a…
We consider simultaneously identifying the membership and locations of point sources that are convolved with different low-pass point spread functions, from the observation of their superpositions. This problem arises in three-dimensional…
Metamaterial homogenization theories usually start with crude approximations that are valid in certain limits in zero order, such as small frequencies, wave vectors and material fill fractions. In some cases they remain surprisingly robust…
We present a non-staggered method for the Maxwell equations in adaptively refined grids. The code is based on finite volume central scheme that preserves in a discrete form both divergence-free property of magnetic field and the Gauss law.…
We present and compare third- as well as fifth-order accurate finite difference schemes for the numerical solution of the compressible ideal MHD equations in multiple spatial dimensions. The selected methods lean on four different…
This work introduces a methodology to solve ordinary differential equations using the Schur decomposition of the linear representation of the differential equation. This is done by first transforming the system into an upper triangular…
MaxCut is a canonical NP-hard combinatorial optimization problem in graph theory with broad applications ranging from physics to bioinformatics. Although variational quantum algorithms offer promising new approaches that may eventually…
Discontinuous Galerkin methods are developed for solving the Vlasov-Maxwell system, methods that are designed to be systematically as accurate as one wants with provable conservation of mass and possibly total energy. Such properties in…
An algebraic multilevel iteration method for solving system of linear algebraic equations arising in $H(\mathrm{curl})$ and $H(\mathrm{div})$ spaces are presented. The algorithm is developed for the discrete problem obtained by using the…
In this paper we focus on high order finite element approximations of the electric field combined with suitable preconditioners, to solve the time-harmonic Maxwell's equations in waveguide configurations. The implementation of high order…
Hyperspectral remote sensing images (HSIs) are characterized by having a low spatial resolution and a high spectral resolution, whereas multispectral images (MSIs) are characterized by low spectral and high spatial resolutions. These…
In this paper, we develop a provably energy stable and conservative discontinuous spectral element method for the shifted wave equation in second order form. The proposed method combines the advantages and central ideas of very successful…
In this manuscript, we propose matrix- and tensor-oriented methods for the numerical solution of the multidimensional evolutionary space-fractional complex Ginzburg--Landau equation. After a suitable spatial semidiscretization, the…
We developed fast direct solver for 3D Helmholtz and Maxwell equations in layered medium. The algorithm is based on the ideas of cyclic reduction for separable matrices. For the grids with major uniform part (within the survey domain in the…
In this article, we study numerical approximation of eigenvalue problems of the Schr\"{o}dinger operator $\displaystyle -\Delta u + \frac{c^2}{|x|^2}u$. There are three stages in our investigation: We start from a ball of any dimension, in…
While 3D Gaussian splatting (3DGS) offers explicit and efficient scene representations for cone-beam computed tomography reconstruction, conventional photometric optimization inherently suffers from spectral bias under ultra sparse-view…
We propose and analyze an efficient spectral-Galerkin approximation for the Maxwell transmission eigenvalue problem in spherical geometry. Using a vector spherical harmonic expansion, we reduce the problem to a sequence of equivalent…
Phase recovery from the bispectrum is a central problem in speckle interferometry which can be posed as an optimization problem minimizing a weighted nonlinear least-squares objective function. We look at two different formulations of the…
The present paper addresses the numerical solution of turbulent flows with high-order discontinuous Galerkin methods for discretizing the incompressible Navier-Stokes equations. The efficiency of high-order methods when applied to…
In this paper, we develop a new type of accelerated algorithms to solve some classes of maximally monotone equations as well as monotone inclusions. Instead of using Nesterov's accelerating approach, our methods rely on a so-called…
Highly heterogeneous, anisotropic coefficients, e.g. in the simulation of carbon-fibre composite components, can lead to extremely challenging finite element systems. Direct solvers for the resulting large and sparse linear systems suffer…