Related papers: Meshless Approximation and Helmholtz-Hodge Decompo…
The displacement field for three dimensional dynamic elasticity problems in the frequency domain can be decomposed into a sum of a longitudinal and a transversal part known as a Helmholtz decomposition. The Cartesian components of both the…
The vector field of a mixed-monotone system is decomposable via a decomposition function into increasing (cooperative) and decreasing (competitive) components, and this decomposition allows for, e.g., efficient computation of reachable sets…
In this work, we obtain the Helmholtz decomposition for vector fields in Morrey, Zorko, and block spaces over bounded or exterior $C^{1}$ domains. Generally speaking, our proofs rely on a careful interplay of localization, flattening, and…
Decomposing the field scattered by an object into vector spherical harmonics (VSH) is the prime task when discussing its optical properties on more analytical grounds. Thus far, it was frequently required in the decomposition that the…
Hessenberg decomposition is the basic tool used in computational linear algebra to approximate the eigenvalues of a matrix. In this article, we generalize Hessenberg decomposition to continuous matrix fields over topological spaces. This…
We investigate how the divergence-free property of magnetic fields can be exploited to resolve the azimuthal ambiguity present in solar vector magnetogram data, by using line-of-sight and horizontal heliographic derivative information as…
Multiresolution approximation (MRA) of the vector fields on T^3 is studied. We introduced in the Fourier space a triad of vector fields called helical vectors which derived from the spherical coordinate system basis. Utilizing the helical…
Vector calculus in three dimensions with a Euclidian metric is the lingua franca of classical physics, including classical electrodynamics. This article corrects some long-standing imprecision in a fundamental result. Some textbooks assert…
In this paper we continue to study the feasibility of active manipulation of Helmholtz fields and by using an improved and more robust numerical strategy we present a detailed sensitivity analysis for the method proposed in our previous…
A 3-dimensional vector field $B$ is said to be Beltrami vector field (force free-magnetic vector field in physics), if $B\times(\nabla\times B)=0$. Motivated by our investigations on projective an polynomial superflows, and as an important…
In this article, we present a vector field method for the study of solutions to massless relativistic transport equations. Compared to the methodologie developped by Fajman-Joudioux-Smulevici, we remove the Lorentz boosts of the commutation…
We develop a Helmholtz-like theorem for differential forms in Euclidean space $E_{n}$ using a uniqueness theorem similar to the one for vector fields. We then apply it to Riemannian manifolds, $R_{n}$, which, by virtue of the…
We introduce and analyze a virtual element method (VEM) for the Helmholtz problem with approximating spaces made of products of low order VEM functions and plane waves. We restrict ourselves to the 2D Helmholtz equation with impedance…
The separation of acoustic and vortical fluctuations in compressible turbulence becomes ambiguous in thermodynamically inhomogeneous media, where refraction by entropy gradients and shocks can be misclassified as solenoidal content by…
We present a new method for the analysis of electromagnetic scattering from homogeneous penetrable bodies. Our approach is based on a reformulation of the governing Maxwell equations in terms of two uncoupled vector Helmholtz systems: one…
Solving the wave equation is one of the most (if not the most) fundamental problems we face as we try to illuminate the Earth using recorded seismic data. The Helmholtz equation provides wavefield solutions that are dimensionally reduced,…
In this work we present a novel approach for computing correspondences between non-rigid objects, by exploiting a reduced representation of deformation fields. Different from existing works that represent deformation fields by training a…
We introduce an exact analytical solution of the homogeneous space-fractional Helmholtz equation in cylindrical coordinates. This solution, called vector Space-Fractional Bessel Beam (SFBB), has been established from the Lorenz' gauge…
We present a methodology to impose micromechanical constraints, i.e. stress equilibrium at grain and sub-grain scale, to an arbitrary (non-equilibrated) voxelized stress field obtained, for example, by means of synchrotron X-ray diffraction…
The vector electric-field Helmholtz equation, containing cross-polarization terms, is factored to produce both pseudo-differential and exponential operator forms of a three-dimensional, one-way, vector, wave equation for propagation through…