Related papers: Application of the Covariant projection finite ele…
Lecture notes on covariant linear perturbation theory and its applications to inflation, dark energy or matter and the cosmic microwave background.
In this paper, the pressure correctionfinite element method is proposed for the 2D/3D time-dependent thermomicropolarfluid equations. Thefirst-order and second-order backward difference formulas (BDF) are adopted to approximate the time…
We review Maxwell's equations and constitutive relations for 3D bianisotropic media in a generalized form: we consider all four variables and allow for nonzero polarization or magnetization, and also nonzero nonzero magnetic charge or…
Covariant affine integral quantization is studied and applied to the motion of a particle in a punctured plane R^2_\ast=R^2\{0}, for which the phase space is R^2_\ast=R^2\{0}X R^2. We examine the consequences of different quantizer…
We consider here the category of diffeological vector pseudo-bundles, and study a possible extension of classical differential geometric tools on finite dimensional vector bundles, namely, the group of automorphisms, the frame bundle, the…
Semi-discrete and fully discrete mixed finite element methods are considered for Maxwell-model-based problems of wave propagation in linear viscoelastic solid. This mixed finite element framework allows the use of a large class of existing…
The current work describes a proof of concept of a 3D XRF scanner, which is able to perform elemental analysis over the cylindrical surface of geological rock-core and to reconstruct a 1D, 2D and a 3D elemental map of the scanned area. The…
We study finite dimensional representations of the projective modular group. Various explicit dimension formulas are given.
In this work we present the results of a study of the possibility of using a homogeneous basis and a new generalization of coupled modes theory to describe non-periodic structured waveguides. It was shown that for the studied…
A virtual element discretisation for the numerical approximation of the three-field formulation of linear poroelasticity introduced in [R. Oyarz\'ua and R. Ruiz-Baier, Locking-free finite element methods for poroelasticity, SIAM J. Numer.…
We consider finite element approximations of the Maxwell eigenvalue problem in two dimensions. We prove, in certain settings, convergence of the discrete eigenvalues using Lagrange finite elements. In particular, we prove convergence in…
The strictly gauge invariant approach to the construction of the analog of guiding center integrals of motion in spatially homogeneous/inhomogeneous constant magnetic fields is considered. With their help the gauge invariant equations,…
Methods for solving Maxwell's equations are integral part of optical metrology and computational lithography setups. Applications require accurate geometrical resolution, high numerical accuracy and/or low computation times. We present a…
Lattice mismatch in layered semiconductor structures with submicron length scales leads to extremely high nonuniform strains. This paper presents a finite element technique for incorporating the effects of the nonuniform strain into an…
We propose an implementation of linear finite element method for nonlocal diffusion problem in 2D space. In the implementation, we reduce the integral from 4D to 2D which would simplify the computation significantly.
We apply high-order mixed finite element discretization techniques and their associated preconditioned iterative solvers to the Variable Eddington Factor (VEF) equations in two spatial dimensions. The mixed finite element VEF…
Several novel imaging and non-destructive testing technologies are based on reconstructing the spatially dependent coefficient in an elliptic partial differential equation from measurements of its solution(s). In practical applications, the…
Free-space light beams with complex intensity patterns, or non-trivial phase structure, are demanded in diverse fields, ranging from classical and quantum optical communications, to manipulation and imaging of microparticles and cells.…
A powerful data transformation method named guided projections is proposed creating new possibilities to reveal the group structure of high-dimensional data in the presence of noise variables. Utilising projections onto a space spanned by a…
We construct finite element subspaces of the space of symmetric tensors with square-integrable divergence on a three-dimensional domain. These spaces can be used to approximate the stress field in the classical Hellinger--Reissner mixed…