Related papers: High-Resolution Solvers for 3D Helmholtz Scatterin…
The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit…
In this paper, we explore the anomalous dispersive relations, inverse scattering transform and fractional N-soliton solutions of the integrable fractional higher-order nonlinear Schrodinger (fHONLS) equations, containing the fractional…
The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an…
The Helmholtz equation is fundamental to wave modeling in acoustics, electromagnetics, and seismic imaging, yet high-frequency regimes remain challenging due to the ``pollution effect''. We propose FD-MGDL, an adaptive framework integrating…
We developed a fast numerical algorithm for solving the three dimensional vectorial Helmholtz equation that arises in electromagnetic scattering problems. The algorithm is based on electric field integral equations and is essentially a…
This paper addresses the efficient solution of linear systems arising from curl-conforming finite element discretizations of $H(\mathrm{curl})$ elliptic problems with heterogeneous coefficients. We first employ the discrete form of a…
We introduce a new class of preconditioners to enable flexible GMRES to find a least-squares solution, and potentially the pseudoinverse solution, of large-scale sparse, asymmetric, singular, and potentially inconsistent systems. We develop…
Finite element methods are effective for Helmholtz problems involving complex geometries and heterogeneous media. However, the resulting linear systems are often large, indefinite, and challenging for iterative solvers, particularly at high…
The advent of massively parallel supercomputers, with their distributed-memory technology using many processing units, has favored the development of highly-scalable local low-order solvers at the expense of harder-to-scale global very…
In this paper, we present a data-driven approach to iteratively solve the discrete heterogeneous Helmholtz equation at high wavenumbers. In our approach, we combine classical iterative solvers with convolutional neural networks (CNNs) to…
We present a polynomial preconditioner for solving large systems of linear equations. The polynomial is derived from the minimum residual polynomial (the GMRES polynomial) and is more straightforward to compute and implement than many…
The emergence of long-offset sparse stationary-recording surveys carried out with ocean bottom nodes (OBN) makes frequency-domain full waveform inversion (FWI) attractive to manage compact volume of data and perform attenuation imaging. One…
In this work, we develop a novel hybrid Schwarz method, termed as edge multiscale space based hybrid Schwarz (EMs-HS), for solving the Helmholtz problem with large wavenumbers. The problem is discretized using $H^1$-conforming nodal finite…
We present a monolithic geometric multigrid preconditioner for solving fluid-solid interaction problems in Stokes limit. The problems are discretized by a spatially adaptive high-order meshless method, the generalized moving least squares…
We propose here a novel stabilization strategy for the PMCHWT equation that cures its frequency and conductivity related instabilities and is obtained by leveraging quasi-Helmholtz projectors. The resulting formulation is well-conditioned…
We present a fast direct solver for boundary integral equations on complex surfaces in three dimensions using an extension of the recently introduced recursive strong skeletonization scheme. For problems that are not highly oscillatory, our…
This paper concerns robust numerical treatment of an elliptic PDE with high contrast coefficients, for which classical finite-element discretizations yield ill-conditioned linear systems. This paper introduces a procedure by which the…
This article presents novel numerical algorithms based on pseudodifferential operators for fast, direct, solution of the Helmholtz equation in 1D, 2D, and 3D inhomogeneous unbounded media. The proposed approach relies on an Operator Fourier…
Computations of incompressible flows with velocity boundary conditions require solution of a Poisson equation for pressure with all Neumann boundary conditions. Discretization of such a Poisson equation results in a rank-deficient matrix of…
We propose a novel finite-difference time-domain (FDTD) scheme for the solution of the Maxwell's equations in which linear dispersive effects are present. The method uses high-order accurate approximations in space and time for the…