Related papers: A boundary integral method for 3D nonuniform diele…
An iterative solution method for fully nonlinear boundary value problems governing self-similar flows with a free boundary is presented. Specifically, the method is developed for application to water entry problems, which can be studied…
A thin two-layered waveguide is considered. The governing equations for this waveguide is a matrix Klein--Gordon equation of dimension~2. A formal solution of this system in the form of a double integral can be obtained by using Fourier…
An efficient surface integral equation-based method is proposed for the analysis of electromagnetic scattering from multilayered media containing complex periodic inclusions. The proposed method defines equivalent currents at the interfaces…
We present a method for calculating the transmission spectra, dispersion, and time delay characteristics of optical-waveguide gratings based on Green's functions and Dyson's equation. Starting from the wave equation for transverse electric…
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…
Seismic full-waveform inversion (FWI) provides high resolution images of the subsurface by exploiting information in the recorded seismic waveforms. This is achieved by solving a highly nonnlinear and nonunique inverse problem. Bayesian…
This paper tests a dielectric model for variation of hydration free energy with geometry of complex solutes in water. It works out some basic aspects of the theory of boundary integral methods for these problems. One aspect of the…
This paper provides a new analytical method to obtain Green's functions of linear dispersive partial differential equations. The Euler-Bernoulli beam equation and the one-dimensional heat conduction equation (dissipation equation) under…
This work presents an unfitted boundary algebraic equation (BAE) method for solving three-dimensional elliptic partial differential equations on complex geometries using finite difference on structured meshes. We demonstrate that replacing…
Acoustic wave propagation through a homogeneous material embedded in an unbounded medium can be formulated as a boundary integral equation and accurately solved with the boundary element method. The computational efficiency deteriorates at…
The single-particle Green's function (GF) of mesoscopic structures plays a central role in mesoscopic quantum transport. The recursive GF technique is a standard tool to compute this quantity numerically, but it lacks physical transparency…
We theoretically investigate the electronic transport properties of curved graphene waveguides by employing non-equilibrium Green's function techniques. We systematically study the dependence of the confined waveguide modes on the potential…
Consider the incidence of a time-harmonic electromagnetic plane wave onto a biperiodic dielectric grating, where the surface is assumed to be a small and smooth perturbation of a plane. The diffraction is modeled as a transmission problem…
Spherical deep learning has been widely applied to a broad range of real-world problems. Existing approaches often face challenges in balancing strong spherical geometric inductive biases with the need to model real-world heterogeneity. To…
In this paper we present and analyse a discontinuous Galerkin finite element method (DGFEM) for the approximation of solutions to elliptic partial differential equations in nondivergence form, with oblique boundary conditions, on curved…
The resolution of the Green's function for obtaining the electrostatic potential generated by the charges located in the dielectric layer of a rectangular waveguide requires efficient integration techniques. Due to the characteristics and…
In the present paper a method of finding the dynamics of the Wigner function of a particle in an infinite quantum well is developed. Starting with the problem of a reflection from an impenetrable wall, the obtained solution is then…
The demagnetization field in micromagnetism is given as the gradient of a potential which solves a partial differential equation (PDE) posed in R^d. In its most general form, this PDE is supplied with continuity condition on the boundary of…
Diffusion models have recently shown promise as powerful generative priors for inverse problems. However, conventional applications require solving the full reverse diffusion process and operating on noisy intermediate states, which poses…
Neural operators, which learn mappings between the function spaces, have been applied to solve boundary value problems in various ways, including learning mappings from the space of the forcing terms to the space of the solutions with the…