相关论文: Sinc-based method for an efficient solution in the…

We analyze a class of coupled quantum systems whose dynamics can be understood via two uncoupled, lower-dimensional quantum settings with auxiliary interactions. The general reduction scheme, based on algebraic properties of the potential…

We study the inverse problem of qualitatively recovering a supported cavity in a thin elastic plate governed by the flexural (biharmonic) wave equation, using far-field pattern measurements. We derive a reciprocity principle and a…

We present a fast direct solver for two dimensional scattering problems, where an incident wave impinges on a penetrable medium with compact support. We represent the scattered field using a volume potential whose kernel is the outgoing…

Highly heterogeneous, anisotropic coefficients, e.g. in the simulation of carbon-fibre composite components, can lead to extremely challenging finite element systems. Direct solvers for the resulting large and sparse linear systems suffer…

We propose a mathematical apparatus which converts magnetostatic (Walker) equations into a wave equation by introducing a specific definition of the magnetic refractive index. Its value can be manipulated by adjusting spatial distribution…

In this paper, we propose Fourier pseudospectral methods to solve the variable-order space fractional wave equation and develop an accelerated matrix-free approach for its effective implementation. In constant-order cases, our methods can…

The elucidation of many physical problems in science and engineering is subject to the accurate numerical modelling of complex wave propagation phenomena. Over the last decades, high-order numerical approximation for partial differential…

We exactly solve the (2+1)-dimensional Dirac equation in a constant magnetic field in the presence of a minimal length. Using a proper ansatz for the wave function, we transform the Dirac Hamiltonian into two 2-dimensional non-relativistic…

We present a novel family of continuous, linear time-frequency transforms adaptable to a multitude of (nonlinear) frequency scales. Similar to classical time-frequency or time-scale representations, the representation coefficients are…

A finite difference scheme is presented for the Dirac equation in (1+1)D. It can handle space- and time-dependent mass and potential terms and utilizes exact discrete transparent boundary conditions (DTBCs). Based on a space- and…

Shape optimization based on surface gradients and the Hadarmard-form is considered for a compressible viscous fluid. Special attention is given to the difference between the 'function composition' approach involving local shape derivatives…

The Dirac equation is solved approximately for the Hulthen potential with the pseudospin symmetry for any spin-orbit quantum number $\kappa$ in the position-dependent mass background. Solutions are obtained reducing the Dirac equation into…

It is shown that in the case of the spherically symmetric static backgrounds there is a gauge in which the Dirac equation is manifestly covariant under rotations. This allows us to separate the spherical variables like in the flat…

This paper addresses the inverse source problem for a mixed-type fractional wave-diffusion-wave equation posed in a cylindrical domain. The governing equation involves a time-dependent variable-order fractional derivative, which enables the…

The numerical approximation of some Boussinesq systems in two spatial dimensions is here considered. The differential systems under study are proposed as asymptotic models for the propagation of waves along the interface of two layers of…

A new algorithm is presented for computing a direct solution to a system of consistent linear equations. It produces a minimum norm particular solution, a generalized inverse (of type {124}), and a null space projection operator. In…

A method for solving an inverse spectral problem for the one-dimensional Dirac equation is developed. The method is based on the Gelfand-Levitan equation and the Fourier-Legendre series expansion of the transmutation kernel. A linear…

This work considers the problem of super-resolution. The goal is to resolve a Dirac distribution from knowledge of its discrete, low-pass, Fourier measurements. Classically, such problems have been dealt with parameter estimation methods.…

This paper presents a novel Direct Integration Theorem (DIT), derived as a non-trivial corollary of the classical Central Slice Theorem (CST). The DIT provides a mathematically consistent transition from the continuous to the discrete…

A new gridding technique for the solution of partial differential equations in cubical geometry is presented. The method is based on volume penalization, allowing for the imposition of a cubical geometry inside of its circumscribing sphere.…