Related papers: A Constructive Approach to the Finite Wavelet Fram…
We use a finite-element method to obtain highly converged results for a nano-optical light scattering setup with a non-periodic geometry.
In \cite{AV99}, Antoine and Vandergheynst propose a group-theoretic approach to continuous wavelet frames on the sphere. The frame is constructed from a single so-called admissible function by applying the unitary operators associated to a…
A finite element method is presented to compute time harmonic microwave fields in three dimensional configurations. Nodal-based finite elements have been coupled with an absorbing boundary condition to solve open boundary problems. This…
In this work, we present an efficient numerical implementation of the finite element method for modal analysis that leverages various symmetry operations, including spatial symmetry in point groups and space-time symmetry in…
In this paper, we construct framelets associated with a sequence of quadrature rules on the simplex $T^{2}$ in $\mathbb{R}^{2}$. We give the framelet transforms -- decomposition and reconstruction of the coefficients for framelets of a…
Frames play an important role in various practical problems related to signal and image processing. In this paper, we define computable frames in computable Hilbert spaces and obtain computable versions of some of their characterizations.…
One approach to ease the construction of frames is to first construct local components and then build a global frame from these. In this paper we will show that the study of the relation between a frame and its local components leads to the…
Numerical calculation of modes in dispersive and absorptive systems is performed using the finite element method. The dispersion is tackled in the frame of an extension of Maxwell's equations where auxiliary fields are added to the…
We present a finite element method (FEM) solver for computation of optical resonance modes in VCSELs. We perform a convergence study and demonstrate that high accuracies for 3D setups can be attained on standard computers. We also…
Using a prime element of a local field K of positive characteristic p, the concepts of multiresolution analysis (MRA) and wavelet can be generalized to such a field. We prove a version of the splitting lemma for this setup and using this…
We give a review of modern approaches to constructing formal solutions to integrable hierarchies of mathematical physics, whose coefficients are answers to various enumerative problems. The relationship between these approaches and…
This paper extends and generalizes previous works on constructing combinatorial multivector fields from continuous systems (see [10]) and the construction of combinatorial vector fields from data (see [2]) by introducing an optimization…
This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to…
We describe an algorithm for computing the convex hull of a finite collection of points in the affine building of SL_d(K), for K a field with discrete valuation. These convex hulls describe the relations among a finite collection of…
Finite frame theory has become a powerful tool for many applications of mathematics. In this paper we introduce a new area of research in frame theory: Integer frames. These are frames having all integer coordinates with respect to a fixed…
A Novel Scaled boundary finite element method, initially developed in Civil Engineering, is reformulated for solving boundary value problems in computational electromagnetics.
As constructing multi-D wavelets remains a challenging problem, we propose a new method called prime coset sum to construct multi-D wavelets. Our method provides a systematic way to construct multi-D non-separable wavelet filter banks from…
The study of many problems in additive combinatorics, such as Szemer\'edi's theorem on arithmetic progressions, is made easier by first studying models for the problem in F_p^n for some fixed small prime p. We give a number of examples of…
We provide constructive necessary and sufficient conditions for a family of periodic wavelets to be a Parseval wavelet frame. The criterion generalizes unitary and oblique extension principles. The case of one wavelet generator and…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…