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We present a Fourier--Galerkin framework for the analysis and computation of subwavelength resonances in two-dimensional scattering problems in finite domains. Starting from the boundary integral formulation, we project the operator onto…
In this paper we combine the theory of reproducing kernel Hilbert spaces with the field of collocation methods to solve boundary value problems with special emphasis on reproducing property of kernels. From the reproducing property of…
This paper is contributed to a fast algorithm for Hankel tensor-vector products. For this purpose, we first discuss a special class of Hankel tensors that can be diagonalized by the Fourier matrix, which is called \emph{anti-circulant}…
In contrast to current state-of-the-art methods, such as NSFP [25], which employ deep implicit neural functions for modeling scene flow, we present a novel approach that utilizes classical kernel representations. This representation enables…
Targeting simulations on parallel hardware architectures, this paper presents computational kernels for efficient computations in mortar finite element methods. Mortar methods enable a variationally consistent imposition of coupling…
We propose an iterative solution method for the 3D high-frequency Helmholtz equation that exploits a contour integral formulation of spectral projectors. In this framework, the solution in certain invariant subspaces is approximated by…
We propose a novel method for the efficient and accurate iterative solution of frequency domain integral equations (IEs) that are used for large/multi-scale electromagnetic scattering problems. The proposed method uses a novel…
We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…
Recently, the numerical schemes of the Fokker-Planck equations describing anomalous diffusion with two internal states have been proposed in [Nie, Sun and Deng, arXiv: 1811.04723], which use convolution quadrature to approximate the…
We develop an efficient quantum implementation of an important signal processing algorithm for line spectral estimation: the matrix pencil method, which determines the frequencies and damping factors of signals consisting of finite sums of…
It is well known that the modulus of the far-field pattern (or phaseless far-field pattern) is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field, so the shape but not the location…
This paper deals with the kernel-based approximation of a multivariate periodic function by interpolation at the points of an integration lattice -- a setting that, as pointed out by Zeng, Leung, Hickernell (MCQMC2004, 2006) and Zeng,…
We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…
Finite Rate of Innovation (FRI) sampling techniques provide efficient frameworks for reconstructing signals with inherent sparsity at rates below Nyquist. However, traditional FRI reconstruction methods rely heavily on pre-defined kernels,…
The problem of approximating a sampled function using sums of a fixed number of complex exponentials is considered. We use alternating projections between fixed rank matrices and Hankel matrices to obtain such an approximation. Convergence,…
Within the expansive domain of optical sciences, achieving the precise characterization of light beams stands as a fundamental pursuit, pivotal for various applications, including telecommunications and imaging technologies. This study…
We describe a method for calculating the roots of special functions satisfying second order linear ordinary differential equations. It exploits the recent observation that the solutions of a large class of such equations can be represented…
Quantum kernel methods have emerged as a promising approach for leveraging high-dimensional feature spaces in machine learning, particularly in domains where classical kernel methods face scalability limitations. In this work, we present…
This note proposes rapidly convergent computational formulae for evaluating scattering kernels from radiative transfer theory. The approach used here does not rely on Legendre expansions, but rather uses exponentially convergent numerical…
We prove a useful formula and new properties for the recently introduced power fractional calculus with non-local and non-singular kernels. In particular, we prove a new version of Gronwall's inequality involving the power fractional…