相关论文: Numerical Computation of approximate Generalized P…
The notion of the Moore-Penrose inverse of tensors with the Einstein product was introduced, very recently. In this paper, we further elaborate this theory by producing a few characterizations of different generalized inverses of tensors. A…
We introduce the concept of mode-k generalized eigenvalues and eigenvectors of a tensor and prove some properties of such eigenpairs. In particular, we derive an upper bound for the number of equivalence classes of generalized tensor…
A full-wave numerical scheme of polarisability tensors evaluation is presented. The method accepts highly conducting bodies of arbitrary shape and explicitly accounts for the radiation as well as ohmic losses. The method is verified on…
A conducting two-dimensional periodic composite of two anisotropic phases with anisotropic, not necessarily symmetric, conductivity tensors is considered. By finding approximate representations for the relevant operators, an approximation…
In this paper, we present a method to retrieve tensor polarizabilities of general bi-anisotropic particles from their far-field responses to plane-wave illuminations. The necessary number of probing excitations and the directions where the…
Compact general formulae for the energy, momentum and angular momentum radiated by confined systems of charges and currents are presented in terms of their multipole Cartesian tensors. Besides the usual electric and magnetic multipoles, a…
The vacuum polarization tensor in strong external magnetic fields has been evaluated numerically for various strengths of magnetic fields and momenta of photons under the threshold of the $e^{\pm}$ pair creation. The fitting formula has…
In this paper, we propose the tensor Noda iteration (NI) and its inexact version for solving the eigenvalue problem of a particular class of tensor pairs called generalized $\mathcal{M}$-tensor pairs. A generalized $\mathcal{M}$-tensor pair…
In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the…
Tessellations are an important tool to model the microstructure of cellular and polycrystalline materials. Classical tessellation models include the Voronoi diagram and Laguerre tessellation whose cells are polyhedra. Due to the convexity…
In this paper, the generalized eigenvalue complementarity problem for tensors (GEiCP-T) is addressed, which arises from the stability analysis of finite dimensional mechanical systems and find applications in differential dynamical systems.…
For many inverse parameter problems for partial differential equations in which the domain contains only well-separated objects, an asymptotic solution to the forward problem involving 'polarization tensors' exists. These are functions of…
This paper studies symmetric tensor decompositions. For symmetric tensors, there exist linear relations of recursive patterns among their entries. Such a relation can be represented by a polynomial, which is called a generating polynomial.…
This paper aims at bridging existing theories in numerical and analytical homogenization. For this purpose the multiscale method of M{\aa}lqvist and Peterseim [Math. Comp. 2014], which is based on orthogonal subspace decomposition, is…
We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and…
Polarization tensor corresponding to near zero volume inhomogeneities was introduced in the pioneering work by Capdeboscq-Vogelius \cite{CV1,CV2}. A beautiful application of the polarization tensor to an inverse problem involving…
We generalize the embedding formalism for conformal field theories to the case of general operators with mixed symmetry. The index-free notation encoding symmetric tensors as polynomials in an auxiliary polarization vector is extended to…
A new technique towards finding asymptotic normalization coefficients in the complex-ranged Gaussian basis is presented. It is shown that a diagonalisation procedure for the total Hamiltonian matrix in the given basis results in…
We propose the fast semi-analytical method of modelling the polarization curves in the voltammetric experiment. The method is based on usage of the special func- tions and shows a big calculation speed and a high accuracy and stability. Low…
We give a full description of the numerical solution of a general charge transport model for doped disordered semiconductors with arbitrary field- and density-dependent mobilities. We propose a suitable scaling scheme and generalize the…