Related papers: Solving 2-D Helmholtz equation in the rectangular,…
In this paper we generalize and improve a recently developed domain decomposition preconditioner for the iterative solution of discretized Helmholtz equations. We introduce an improved method for transmission at the internal boundaries…
In this paper, based on the combination of tensor neural network and a posteriori error estimator, a novel type of machine learning method is proposed to solve high-dimensional boundary value problems with homogeneous and non-homogeneous…
Two boundary value problems for the Helmholtz equation in a semi-infinite strip are considered. The main feature of these problems is that, in addition to the function and its normal derivative on the boundary, the functionals of the…
In this work, we present a new solution representation for the Helmholtz transmission problem in a bounded domain in $\mathbb{R}^2$ with a thin and periodic layer of finite length. The layer may consists of a periodic pertubation of the…
We present an efficient procedure for computing resonances and resonant modes of Helmholtz problems posed in exterior domains. The problem is formulated as a nonlinear eigenvalue problem (NEP), where the nonlinearity arises from the use of…
Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…
We present a collection of integral equation methods for the solution to the two-dimensional, modified Helmholtz equation, $u(\x) - \alpha^2 \Delta u(\x) = 0$, in bounded or unbounded multiply-connected domains. We consider both Dirichlet…
In a recent paper \cite{chak} Chakraborty et al have put forward a perturbative formulation for solving the 2 dimensional homogeneous Helmholtz equation with the Dirichlet condition on a supercircular boundary. In this note a single…
Photonic computing has recently become an interesting paradigm for high-speed calculation of computing processes using light-matter interactions. Here, we propose and study an electromagnetic wave-based structure with the ability to…
We proposed a framework for solving inverse problems in differential equations based on neural networks and automatic differentiation. Neural networks are used to approximate hidden fields. We analyze the source of errors in the framework…
The calculation of a three-dimensional underwater acoustic field has always been a key problem in computational ocean acoustics. Traditionally, this solution is usually obtained by directly solving the acoustic Helmholtz equation using a…
Solving PDEs with machine learning techniques has become a popular alternative to conventional methods. In this context, Neural networks (NNs) are among the most commonly used machine learning tools, and in those models, the choice of an…
The double-layer potential plays an important role in solving boundary value problems for elliptic equations, and in the study of which for a certain equation, the properties of the fundamental solutions of the given equation are used. All…
We present algorithms for solving high-frequency acoustic scattering problems in complex domains. The eikonal and transport partial differential equations from the WKB/geometric optic approximation of the Helmholtz equation are solved…
We propose a new method to deal with the essential boundary conditions encountered in the deep learning-based numerical solvers for partial differential equations. The trial functions representing by deep neural networks are…
We analyse parallel overlapping Schwarz domain decomposition methods for the Helmholtz equation, where the subdomain problems satisfy first-order absorbing (impedance) transmission conditions, and exchange of information between subdomains…
A sound field estimation method based on a physics-informed convolutional neural network (PICNN) using spline interpolation is proposed. Most of the sound field estimation methods are based on wavefunction expansion, making the estimated…
In this paper, we study the nonlinear periodic Westervelt equation with excitations located within a bounded domain in $\mathbb{R}^d$, where $d \in \{2,3\}$, subject to Robin boundary conditions. This problem is of particular interest for…
This paper presents smoothed combined field integral equations for the solution of Dirichlet and Neumann exterior Helmholtz problems. The integral equations introduced in this paper are smooth in the sense that they only involve…
In this paper, we propose a novel machine learning-based method to solve the acoustic scattering problem in unbounded domain. We first employ the Dirichlet-to-Neumann (DtN) operator to truncate the physically unbounded domain into a…