Related papers: Linearly scalable fast direct solver based on prox…
This paper introduces a smoothed proximal Lagrangian method for minimizing a nonconvex smooth function over a convex domain with additional explicit convex nonlinear constraints. Two key features are 1) the proposed method is single-looped,…
With the stagnation of processor core performance, further reductions in the time-to-solution for geophysical fluid problems are becoming increasingly difficult with standard time integrators. Parallel-in-time exposes and exploits…
A numerical method for solving the equations modeling acoustic scattering is presented. The method is capable of handling several dozen scatterers, each of which is several wave-lengths long, on a personal work station. Even for geometries…
We introduce an efficient numerical method for second order linear ODEs whose solution may vary between highly oscillatory and slowly changing over the solution interval. In oscillatory regions the solution is generated via a nonoscillatory…
In this paper, we use a straightforward numerical method to solve scattering models in one-dimensional lattices based on a tight-binding band structure. We do this by using the wave packet approach to scattering, which presents a more…
This paper presents a direct solution technique for the scattering of time-harmonic waves from a bounded region of the plane in which the wavenumber varies smoothly in space.The method constructs the interior Dirichlet-to-Neumann (DtN) map…
Although some preconditioners are available for solving dense linear systems, there are still many matrices for which preconditioners are lacking, in particular in cases where the size of the matrix $N$ becomes very large. There remains…
We present a new framework for the fast solution of inhomogeneous elliptic boundary value problems in domains with smooth boundaries. High-order solvers based on adaptive box codes or the fast Fourier transform can efficiently treat the…
The generalized Debye source representation of time-harmonic electromagnetic fields yields well-conditioned second-kind integral equations for a variety of boundary value problems, including the problems of scattering from perfect electric…
Propagation of P and SV waves in an elastic solid containing randomly distributed inclusions in a half-space is investigated. The approach is based on a multiple scattering analysis similar to the one proposed by Fikioris and Waterman for…
We consider an inverse elastic scattering problem of simultaneously reconstructing a rigid obstacle and the excitation sources using near-field measurements. A two-phase numerical method is proposed to achieve the co-inversion of multiple…
We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply-connected fluid domain that includes…
We consider global efficiency of algorithms for minimizing a sum of a convex function and a composition of a Lipschitz convex function with a smooth map. The basic algorithm we rely on is the prox-linear method, which in each iteration…
Solving the radiative transfer equation with the discrete ordinates (S$_N$) method leads to a non-physical imprint of the chosen quadrature set on the solution. To mitigate these so-called ray effects, we propose a modification of the S$_N$…
In this work we consider the inverse elastic scattering problem by an inclusion in two dimensions. The elastic inclusion is placed in an isotropic homogeneous elastic medium. The inverse problem, using the third Betti's formula (direct…
We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The fundamental principles from the earlier work are retained:…
Consider the scattering of a time-harmonic elastic plane wave by a periodic rigid surface. The elastic wave propagation is governed by the two-dimensional Navier equation. Based on a Dirichlet-to-Neumann (DtN) map, a transparent boundary…
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…
A discretization scheme for variable coefficient Helmholtz problems on two-dimensional domains is presented. The scheme is based on high-order spectral approximations and is designed for problems with smooth solutions. The resulting system…
We study bilevel optimization with a fixed polyhedral lower feasible set. Such problems are challenging for two reasons: active-set changes can make the upper objective nonsmooth, and existing hypergradient methods typically require…