Related papers: Domain Decomposition with Neural Network Interface…
In this paper, we present an accurate numerical method for the time-harmonic Maxwell's equations for bi-periodic multilayered media with quasi-periodic incident waves using the Method of Fundamental Solutions in conjunction with a…
The time domain enclosure method is one of analytical methods for inverse obstacle problems governed by partial differential equations in the time domain. This paper considers the case when the governing equation is given by the Maxwell…
Recent developments in mechanical, aerospace, and structural engineering have driven a growing need for efficient ways to model and analyse structures at much larger and more complex scales than before. While established numerical methods…
This paper concerns the numerical resolution of a data completion problem for the time-harmonic Maxwell equations in the electric field. The aim is to recover the missing data on the inaccessible part of the boundary of a bounded domain…
An efficient finite-difference time-domain (FDTD) algorithm is built to solve the transverse electric 2D Maxwell's equations with inhomogeneous dielectric media where the electric fields are discontinuous across the dielectric interface.…
This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…
We present a meshless Schwarz-type non-overlapping domain decomposition method based on artificial neural networks for solving forward and inverse problems involving partial differential equations (PDEs). To ensure the consistency of…
We present both, theory and an algorithm for solving time-harmonic wave problems in a general setting. The time-harmonic solutions will be achieved by computing time-periodic solutions of the original wave equations. Thus, an exact…
Maxwell's equations, a system of linear partial differential equations (PDEs), describe the behavior of electric and magnetic fields in time and space and are essential for many important electromagnetic applications. Although numerical…
This paper proposes a deep-learning-based domain decomposition method (DeepDDM), which leverages deep neural networks (DNN) to discretize the subproblems divided by domain decomposition methods (DDM) for solving partial differential…
Several neural network approaches for solving differential equations employ trial solutions with a feedforward neural network. There are different means to incorporate the trial solution in the construction, for instance one may include…
This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing…
In this paper we present an overview of recent progress on the development and analysis of domain decomposition preconditioners for discretised Helmholtz problems, where the preconditioner is constructed from the corresponding problem with…
We propose a new methodology for parametric domain decomposition using iterative principal component analysis. Starting with iterative principle component analysis, the high dimension manifold is reduced to the lower dimension manifold.…
Deep learning is emerging as a new paradigm for solving inverse imaging problems. However, the deep learning methods often lack the assurance of traditional physics-based methods due to the lack of physical information considerations in…
The transferable neural network (TransNet) is a two-layer shallow neural network with pre-determined and uniformly distributed neurons in the hidden layer, and the least-squares solvers can be particularly used to compute the parameters of…
With recent advancements in computer hardware and software platforms, there has been a surge of interest in solving partial differential equations with deep learning-based methods, and the integration with domain decomposition strategies…
Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…
Deep learning-based methods deliver state-of-the-art performance for solving inverse problems that arise in computational imaging. These methods can be broadly divided into two groups: (1) learn a network to map measurements to the signal…
We propose a primal-dual parallel proximal splitting method for solving domain decomposition problems for partial differential equations. The problem is formulated via minimization of energy functions on the subdomains with coupling…