Related papers: Using B-spline frames to approximate solutions of …
We give a principled approach for the selection of a boundary integral, retarded potential representation for the solution of scattering problems for the wave equation in an exterior domain.
A periodizing scheme and the method of fundamental solutions are used to solve acoustic wave scattering from doubly-periodic three-dimensional multilayered media. A scattered wave in a unit cell is represented by the sum of the near and…
Redundant Gabor frames admit an infinite number of dual frames, yet only the canonical dual Gabor system, constructed from the minimal l2-norm dual window, is widely used. This window function however, might lack desirable properties, e.g.…
The Half-Space Matching (HSM) method has recently been developed as a new method for the solution of 2D scattering problems with complex backgrounds, providing an alternative to Perfectly Matched Layers (PML) or other artificial boundary…
We propose $S^3$LAM, a novel RGB-D SLAM system that leverages 2D surfel splatting to achieve highly accurate geometric representations for simultaneous tracking and mapping. Unlike existing 3DGS-based SLAM approaches that rely on 3D…
In the context of providing a mathematical framework for the propagation of ultrasound waves in a random multiscale medium, we consider the scattering of classical waves (modeled by a divergence form scalar Helmholtz equation) by a bounded…
A classical problem in acoustic (and electromagnetic) scattering concerns the evaluation of the Green's function for the Helmholtz equation subject to impedance boundary conditions on a half-space. The two principal approaches used for…
Recent experimental work has demonstrated the potential to combine the merits of diffractive and on-chip photonic information processing devices in a single chip by making use of planar (or slab) waveguides. Researchers have adapted key…
Gaussian Splatting has rapidly emerged as a transformative technique for real-time 3D scene representation, offering a highly efficient and expressive alternative to Neural Radiance Fields (NeRF). Its ability to render complex scenes with…
In simulation technology, computationally expensive objective functions are often replaced by cheap surrogates, which can be obtained by interpolation. Full grid interpolation methods suffer from the so-called curse of dimensionality,…
In the field of optics and nanophotonics, simulation of electromagnetic scattering plays a major role in the study of complex nanostructures and optical devices. The numerical analysis of scattering spectra, even for nanocavities with…
Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing.…
Multipole expansion of an incident radiation field - that is, representation of the fields as sums of vector spherical wavefunctions - is essential for theoretical light scattering methods such as the T-matrix method and generalised…
An efficient method for frequency domain analysis of 2D cross-field devices is presented. This work was done to analyze and design high efficiency magnetrons. Arbitrary device-geometries are described by a piecewise planar boundary. The…
When modeling propagation and scattering phenomena using integral equations discretized by the boundary element method, it is common practice to approximate the boundary of the scatterer with a mesh comprising elements of size approximately…
An Isogeometric Boundary Element Method (IgA-BEM) is considered for the numerical solution of Helmholtz problems on 3D bounded or unbounded domains, admitting a smooth conformal multi-patch representation of their finite boundary surface.…
Optical scatterometry is a method to measure the size and shape of periodic micro- or nanostructures on surfaces. For this purpose the geometry parameters of the structures are obtained by reproducing experimental measurement results…
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This approach is useful for a higher…
We describe some recent advances in the numerical solution of acoustic scattering problems. A major focus of the paper is the efficient solution of high frequency scattering problems via hybrid numerical-asymptotic boundary element methods.…
We propose a novel iterative numerical method to solve the three-dimensional inverse obstacle scattering problem of recovering the shape of the obstacle from far-field measurements. To address the inherent ill-posed nature of the inverse…