Related papers: Wavelets for Elliptical Waveguide Problems
In this paper we discuss the use of wavelet bases to solve the relativistic three-body problem. Wavelet bases can be used to transform momentum-space scattering integral equations into an approximate system of linear equations with a sparse…
Numerical transfer matrices have been widely used in the study of wave propagation and scattering. These may be viewed as descretizations of a recently introduced fundamental notion of transfer matrix which admits a representation in terms…
We demonstrate a wide range of novel functions in integrated, CMOS compatible, devices. This platform has promise for telecommunications and on-chip WDM optical interconnects for computing.
We consider a class of convergence questions for infinite products that arise in wavelet theory when the wavelet filters are more singular than is traditionally built into the assumptions. We establish pointwise convergence properties for…
Investigation of light in the waveguide structures is a topical modern problem that has long historical roots. A parallel-plate waveguide is a base model in these studies and it is intensively used in numerous investigations of nanooptics,…
A procedure to obtain differentiation matrices is extended straightforwardly to yield new differentiation matrices useful to obtain derivatives of complex rational functions. Such matrices can be used to obtain numerical solutions of some…
A new approach to prove the one-dimensional Cauchy problem's weakly discontinuous solutions for hyperbolic PDEs are on the characteristics is discussed in this paper. To do so, I use wavelet singularity detection methods or WTMM [1] based…
As a main research area in applied and computational harmonic analysis, the theory and applications of framelets have been extensively investigated. Most existing literature is devoted to framelet systems that only use one dilation matrix…
A numerical technique is described that can efficiently compute solutions in interface problems. These are problems with data, such as the coefficients of differential equations, discontinuous or even singular across one or more interfaces.…
In this paper we present a general approach to multivariate periodic wavelets generated by scaling functions of de la Vall\'ee Poussin type. These scaling functions and their corresponding wavelets are determined by their Fourier…
This paper investigates an adaptive wavelet collocation time domain method for the numerical solution of Maxwell's equations. In this method a computational grid is dynamically adapted at each time step by using the wavelet decomposition of…
We discuss the propagation of electromagnetic waves on a rectangular lattice of polarizable point dipoles. For wavelengths long compared to the lattice spacing, we obtain the dispersion relation in terms of the lattice spacing and the…
In current work, non-familiar shifted Lucas polynomials are introduced. We have constructed a computational wavelet technique for solution of initial/boundary value second order differential equations. For this numerical scheme, we have…
This paper describes a method for extracting rapidly varying, superimposed amplitude- and frequency-modulated signal components. The method is based upon the continuous wavelet transform (CWT) and uses a new wavelet which is a modification…
This article proposes a novel approach for determining exact solutions to nonlinear ordinary differential equations. The recommended iterative method provides the solution via a rapidly converging series that readily approaches a closed…
An asymptotic investigation of monochromatic electromagnetic fields in a layered periodic medium is carried out under the assumption that the wave frequency is close to the frequency of a stationary point of the dispersion surface. We find…
An efficient and expressive wavefunction ansatz is key to scalable solutions for complex many-body electronic structures. While Slater determinants are predominantly used for constructing antisymmetric electronic wavefunction ans\"{a}tze,…
We consider the applications of a numerical-analytical approach based on multiscale variational wavelet technique to the systems with collective type behaviour described by some forms of Vlasov-Poisson/Maxwell equations. We calculate the…
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.
We introduce a layer potential representation for the solution of the transmission problem defined by two dielectric channels, or open wave-guides, meeting along the straight-line interface, $\{x_1=0\}.$ The main observation is that the…