Related papers: A modal approach for the solution of the non-linea…
Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the…
Periodic micromagnetic finite element method (PM-FEM) is introduced to solve periodic unit cell problems using the Landau-Lifshitz-Gilbert equation. PM-FEM is applicable to general problems with 1D, 2D, and 3D periodicities. PM-FEM is based…
The nonlinear Fourier transform (NFT), a powerful tool in soliton theory and exactly solvable models, is a method for solving integrable partial differential equations governing wave propagation in certain nonlinear media. The NFT…
We introduce a versatile numerical method for modeling light diffraction in periodically patterned photonic structures containing quadratically nonlinear non-centrosymmetric optical materials. Our approach extends the generalized source…
In this paper we propose a new formulation of the Fourier Modal Method based on an alternative treatment of interface conditions allowing us to overcome the effect of the Gibbs phenomenon. Explicit consideration of the interface conditions…
We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…
We propose an efficient algorithm for the evaluation of the potential and its gradient of gravitational/electrostatic $N$-body systems, which we call particle mesh multipole method (PMMM or PM$^3$). PMMM can be understood both as an…
This paper presents a novel formulation and consequently a new solution for two dimensional TM electromagnetic integral equations by the method of moments in polar coordination. The main idea is the reformulation of the 2-D problem…
An analytic solution to a stationary heat conduction problem in 2D unbounded doubly periodic composite materials with temperature dependent conductivities of their components is given. Corresponding nonlinear boundary value problem is…
This article introduces a novel approach to learning monotone neural networks through a newly defined penalization loss. The proposed method is particularly effective in solving classes of variational problems, specifically monotone…
In the article the problem of output setpoint tracking for affine non-linear system is considered. Presented approach combines state feedback linearization and homotopy numerical continuation in subspaces of phase space where feedback…
The output of physical systems is often accessible by measurements such as the 3D position of a robotic arm actuated by many actuators or the speckle patterns formed by shining the spot of a laser pointer on a wall. The selection of the…
This paper proposes a fast time-domain boundary element method (TDBEM) to solve three-dimensional transient electromagnetic scattering problems regarding perfectly electric conductors in the classical marching-on-in-time manner. The…
In this paper, a fast multipole method (FMM) is proposed for 3-D Laplace equation in layered media. The potential due to charges embedded in layered media is decomposed into a free space component and four types of reaction field…
The Laplace-Beltrami problem on closed surfaces embedded in three dimensions arises in many areas of physics, including molecular dynamics (surface diffusion), electromagnetics (harmonic vector fields), and fluid dynamics (vesicle…
A Lagrangian numerical scheme for solving nonlinear degenerate Fokker-Planck equations in space dimensions $d\ge2$ is presented. It applies to a large class of nonlinear diffusion equations, whose dynamics are driven by internal energies…
We describe a mechanism by which both ferroelectric polarization and magnetization can be created in nonpolar, nonmagnetic materials. Using a combination of phenomenological modeling and first-principles calculations, we demonstrate that…
The capability to incorporate moving geometric features within models for complex simulations is a common requirement in many fields. Fluid mechanics within aeronautical applications, for example, routinely feature rotating (e.g. turbines,…
We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral…
Three kinds of Fragile Points Methods based on Petrov-Galerkin weak-forms (PG-FPMs) are proposed for analyzing heat conduction problems in nonhomogeneous anisotropic media. This is a follow-up of the previous study on the original FPM based…