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Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for higher dimensional problems such as in textures, crystallography, and quantum mechanics. Large…
High-dimensional Partial Differential Equations (PDEs) are a popular mathematical modelling tool, with applications ranging from finance to computational chemistry. However, standard numerical techniques for solving these PDEs are typically…
We present a high-order accurate boundary-based solver for three-dimensional (3D) frequency-domain scattering from a doubly-periodic grating of smooth axisymmetric sound-hard or transmission obstacles. We build the one-obstacle solution…
Tensor train (TT) representation has achieved tremendous success in visual data completion tasks, especially when it is combined with tensor folding. However, folding an image or video tensor breaks the original data structure, leading to…
We introduce the tensor numerical method for solution of the $d$-dimensional optimal control problems with fractional Laplacian type operators in constraints discretized on large $n^{\otimes d}$ tensor-product Cartesian grids. The approach…
Density functional theory (DFT) has emerged as one of the most versatile and lucrative approaches in electronic structure calculations of many-electron systems in past four decades. Here we give an account of the development of a…
The tensor train (TT) format enjoys appealing advantages in handling structural high-order tensors. The recent decade has witnessed the wide applications of TT-format tensors from diverse disciplines, among which tensor completion has drawn…
The Discrete Fourier Transform (DFT) underpins the solution to many inverse problems commonly possessing missing or un-measured frequency information. This incomplete coverage of Fourier space always produces systematic artefacts called…
Tensor Ring (TR) decomposition is a powerful tool for high-order data modeling, but is inherently restricted to discrete forms defined on fixed meshgrids. In this work, we propose a TR functional decomposition for both meshgrid and…
X-ray interferometry is an emerging imaging modality with a wide variety of potential clinical applications, including lung imaging. A grating interferometer uses a diffraction grating to produce a periodic interference pattern and measures…
We analyze classical dimer models on the square and triangular lattice using a tensor network representation of the dimers. The correlation functions are numerically calculated using the recently developed "Tensor renormalization group"…
We propose a Trefftz discontinuous Galerkin (TDG) method for the approximation of plane wave scattering by periodic diffraction gratings, modelled by the two-dimensional Helmholtz equation. The periodic obstacle may include penetrable and…
Tensor decompositions, which represent an $N$-order tensor using approximately $N$ factors of much smaller dimensions, can significantly reduce the number of parameters. This is particularly beneficial for high-order tensors, as the number…
The fast algorithms in Fourier optics have invigorated multifunctional device design and advanced imaging technologies. However, the necessity for fast computations has led to limitations in the widely used conventional Fourier methods,…
Scattering of femtosecond laser pulses on resonant transmission and reflection gratings made of dispersive (Drude metals) and dielectric materials is studied by a time-domain numerical algorithm for Maxwell's theory of linear passive…
Tensor network techniques are becoming increasingly popular tools to solve partial differential equations within the so-called quantics representation. Their popularity stems from the fact that their spatial resolution depends only…
Optimal exploitation of supercomputing resources for the evaluation of electrostatic forces remains a challenge in molecular dynamics simulations of very large systems. The most efficient methods are currently based on particle-mesh Ewald…
Discretizing an analytic function on a uniform real-space grid is often done via a straightforward collocation method. This is ubiquitous in all areas of computational physics and quantum chemistry. An example in Density Functional Theory…
This paper presents an innovative approach to computational acoustic imaging of biperiodic surfaces, exploiting the capabilities of an acoustic superlens to overcome the diffraction limit. We address the challenge of imaging physical…
Gratings and holograms are patterned surfaces that tailor optical signals by diffraction. Despite their long history, variants with remarkable functionalities continue to be discovered. Further advances could exploit Fourier optics, which…