Related papers: Refinement trajectory and determination of eigenst…
In this work, we fully explore three refined convergence structures of the lowest-order rectangular Raviart-Thomas element in solving the Laplace eigenvalue problem. Firstly, the scheme possesses a property of supercloseness between the…
A new set of vector solutions to Maxwell's equations based on solutions to the wave equation in spheroidal coordinates allows laser beams to be described beyond the paraxial approximation. Using these solutions allows us to calculate the…
This paper aims at presenting a new approach to the electro-sensing problem using wavelets. It provides an efficient algorithm for recognizing the shape of a target from micro-electrical impedance measurements. Stability and resolution…
This work introduces a time-adaptive strategy that uses a refinement estimator based on the first Frenet curvature. In dynamics, a time-adaptive strategy is a mechanism that interactively proposes changes to the time step used in iterative…
This review paper is intended to give a useful guide for those who want to apply discrete wavelets in their practice. The notion of wavelets and their use in practical computing and various applications are briefly described, but rigorous…
Even though convolutional neural networks have become the method of choice in many fields of computer vision, they still lack interpretability and are usually designed manually in a cumbersome trial-and-error process. This paper aims at…
The notion of an equational shell is studied to involve the objects and their environment. Appropriate methods are studied as valid embeddings of refined objects. The refinement process determines the linkages between the variety of…
Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…
The optimal wavelet basis is used to develop quantitative, experimentally applicable criteria for self-organization. The choice of the optimal wavelet is based on the model of self-organization in the wavelet tree. The framework of the…
In this paper, we study the convolution structure in the special affine Fourier domain to combine the advantages of the well known special affine Fourier and wavelet transforms into a novel integral transform coined as special affine…
The characterization of particle diffusion is a classical problem in physics and probability theory. The field of microrheology is based on experiments in which microscopic tracer beads are placed into a non-Newtonian fluid and tracked…
In this paper we present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to variational approach in the general case we have the solution as a…
We develop a modal method that solves Maxwell's equations in the presence of the linearized hydrodynamic correction. Using this approach, it is now possible to calculate the full diffraction for structures with period of the order of the…
The eigenmodes of resonating structures, e.g., electromagnetic cavities, are sensitive to deformations of their shape. In order to compute the sensitivities of the eigenpair with respect to a scalar parameter, we state the Laplacian and…
In this paper we describe an adaptive Levin method for numerically evaluating integrals of the form $\int_\Omega f(\mathbf x) \exp(i g(\mathbf x)) \,d\Omega$ over general domains that have been meshed by transfinite elements. On each…
The problem of the harmonic oscillator with a centrally located delta function potential can be exactly solved in one dimension where the eigenfunctions are expressed as superpositions of the Hermite polynomials or as confluent…
We develop an iterative refinement method that improves the accuracy of a user-chosen subset of $k$ eigenvectors ($k\ll n$) of an $n\times n$ real symmetric matrix. Using an orthogonal matrix represented in compact WY form, the method…
A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent…
The concept of refinement from probability elicitation is considered for proper scoring rules. Taking directions from the axioms of probability, refinement is further clarified using a Hilbert space interpretation and reformulated into the…
It is well known that the quasi-optimality of the Galerkin finite element method for the Helmholtz equation is dependent on the mesh size and the wave-number. In the literature, different criteria have been proposed to ensure uniform…