Related papers: Adapting free-space fast multipole method for laye…
Efficient Green's function evaluation in layered media is a holy-grail of wave theory in general and for electromagnetics in particular. While there is a very large amount of knowledge in this context with vast literature, there are yet…
We propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with multi-spatial scales. The method uses decompositions of the…
In this paper we present a locally and dimension-adaptive sparse grid method for interpolation and integration of high-dimensional functions with discontinuities. The proposed algorithm combines the strengths of the generalised sparse grid…
We introduce a new arbitrarily high-order method for the rapid evaluation of hyperbolic potentials (space-time integrals involving the Green's function for the scalar wave equation). With $M$ points in the spatial discretization and $N_t$…
This paper introduces a directional multiscale algorithm for the two dimensional $N$-body problem of the Helmholtz kernel with applications to high frequency scattering. The algorithm follows the approach in [Engquist and Ying, SIAM Journal…
Transposed convolution is crucial for generating high-resolution outputs, yet has received little attention compared to convolution layers. In this work we revisit transposed convolution and introduce a novel layer that allows us to place…
A semiclassical theory of single and multi-mode lasing is derived for open complex or random media using a self-consistent linear response formulation. Unlike standard approaches which use closed cavity solutions to describe the lasing…
In this paper, we propose a new analytic continuation method to extract real frequency spectral functions from imaginary frequency Green's functions of quantum many-body systems. This method is based on the pole representation of Matsubara…
We present a fast, adaptive multiresolution algorithm for applying integral operators with a wide class of radially symmetric kernels in dimensions one, two and three. This algorithm is made efficient by the use of separated representations…
Vortex element methods are often used to efficiently simulate incompressible flows using Lagrangian techniques. Use of the FMM (Fast Multipole Method) allows considerable speed up of both velocity evaluation and vorticity evolution terms in…
We present an optimised multipole algorithm for computing the three-point correlation function (3PCF), tailored for application to large-scale cosmological datasets. The algorithm builds on a $in\, situ$ interpretation of correlation…
Marine Controlled Source Electromagnetic (CSEM) is employed both in large-scale geophysical applications as well as within exploration of hydrocarbons and gas hydrates. Due to the diffusive character of the EM field only very low…
The kernel-independent fast multipole method (KIFMM) proposed in [1] is of almost linear complexity. In the original KIFMM the time-consuming M2L translations are accelerated by FFT. However, when more equivalent points are used to achieve…
Convolution is an efficient technique to obtain abstract feature representations using hierarchical layers in deep networks. Although performing convolution in Euclidean geometries is fairly straightforward, its extension to other…
We present GW calculations of molecules, ordered and disordered solids and interfaces, which employ an efficient contour deformation technique for frequency integration, and do not require the explicit evaluation of virtual electronic…
As aliasing artefacts are highly structural and non-local, many MRI reconstruction networks use pooling to enlarge filter coverage and incorporate global context. However, this inadvertently impedes fine detail recovery as downsampling…
The Helmholtz equation is fundamental to wave modeling in acoustics, electromagnetics, and seismic imaging, yet high-frequency regimes remain challenging due to the ``pollution effect''. We propose FD-MGDL, an adaptive framework integrating…
State-of-the-art learned reconstruction methods often rely on black-box modules that, despite their strong performance, raise questions about their interpretability and robustness. Here, we build on a recently proposed image reconstruction…
Inverse design enables automating the discovery and optimization of devices achieving performance significantly exceeding that of traditional human-engineered designs. However, existing methodologies to inverse-design electromagnetic…
In this paper, we present a multiscale framework for solving the Helmholtz equation in heterogeneous media without scale separation and in the high frequency regime where the wavenumber $k$ can be large. The main innovation is that our…