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A numerical algorithm is presented for solving the direct scattering problems by the Modified Rayleigh Conjecture Method (MRC) introduced by A.G.Ramm. Some numerical examples are given. They show that the method is numerically efficient.
The motivation of this work is an inverse problem for the acoustic wave equation, where an array of sensors probes an unknown medium with pulses and measures the scattered waves. The goal of the inversion is to determine from these…
We present a Multi-Index Quasi-Monte Carlo method for the solution of elliptic partial differential equations with random coefficients. By combining the multi-index sampling idea with randomly shifted rank-1 lattice rules, the algorithm…
A new numerical method for X-ray tomography for a specific case of incomplete Radon data is proposed. Potential applications are in checking out bulky luggage in airports. This method is based on the analysis of the transport PDE governing…
We present a sweeping preconditioner for quasi-optimal Domain Decomposition Methods (DDM) applied to Helmholtz transmission problems in periodic layered media. Quasi-optimal DD (QO DD) for Helmholtz equations rely on transmission operators…
In this letter, we propose a reduced-order model to bridge the particle transport mechanics and the macroscopic fluid dynamics in the highly scattered regime. A rigorous mathematical derivation and a concise physical interpretation are…
The planar-diagrammatic technique of large-$N$ random matrices is extended to evaluate averages over the circular ensemble of unitary matrices. It is then applied to study transport through a disordered metallic ``grain'', attached through…
This article provides a high-level overview of some recent works on the application of quasi-Monte Carlo (QMC) methods to PDEs with random coefficients. It is based on an in-depth survey of a similar title by the same authors, with an…
Quantum learning encounters fundamental challenges when estimating non-linear properties, owing to the inherent linearity of quantum mechanics. Although recent advances in single-copy randomized measurement protocols have achieved optimal…
Accurately simulating photon transport is crucial for non-destructive testing and medical diagnostic applications using X-ray radiography and computed tomography (CT). Solving a discretized form of the linear Boltzmann equation is a…
We propose a matrix model which embodies the semiclassical approach to the problem of quantum transport in chaotic systems. Specifically, a matrix integral is presented whose perturbative expansion satisfies precisely the semiclassical…
Quotient regularization models (QRMs) are a class of powerful regularization techniques that have gained considerable attention in recent years, due to their ability to handle complex and highly nonlinear data sets. However, the nonconvex…
We propose and analyze numerical schemes for the gradient flow of $Q$-tensor with the quasi-entropy. The quasi-entropy is a strictly convex, rotationally invariant elementary function, giving a singular potential constraining the…
We consider a particular class of equations of motion, generalizing to n degrees of freedom the "dissipative spin--orbit problem", commonly studied in Celestial Mechanics. Those equations are formulated in a pseudo-Hamiltonian framework…
For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit…
In this thesis, we present and apply the isomonodromy method (or isomonodromic method) to the study of quasinormal modes (QNMs), more precisely, we consider the analysis of modes that are associated with linear perturbations in two distinct…
Diffuse optical tomography (DOT) is an imaging modality which uses near-infrared light. Although iterative numerical schemes are commonly used for its inverse problem, correct solutions are not obtained unless good initial guesses are…
This paper presents a simple model that mimics quantum mechanics (QM) results without using complex wavefunctions or non-localities. The proposed model only uses integer-valued quantities and arithmetic operations, in particular assuming a…
We discuss an approach to obtaining black hole quasinormal modes (QNMs) using the asymptotic iteration method (AIM), initially developed to solve second order ordinary differential equations. We introduce the standard version of this method…
Quasi-Monte Carlo (QMC) method is a useful numerical tool for pricing and hedging of complex financial derivatives. These problems are usually of high dimensionality and discontinuities. The two factors may significantly deteriorate the…