FMM-LU: A fast direct solver for multiscale boundary integral equations in three dimensions

01/18/2022
by   Daria Sushnikova, et al.
NYU college
Simons Foundation
0

We present a fast direct solver for boundary integral equations on complex surfaces in three dimensions, using an extension of the recently introduced strong recursive skeletonization scheme. For problems that are not highly oscillatory, our algorithm computes an LU-like hierarchical factorization of the dense system matrix, permitting application of the inverse in O(N) time, where N is the number of unknowns on the surface. The factorization itself also scales linearly with the system size, albeit with a somewhat larger constant. The scheme is built on a level-restricted, adaptive octree data structure and therefore it is compatible with highly nonuniform discretizations. Furthermore, the scheme is coupled with high-order accurate locally-corrected Nyström quadrature methods to integrate the singular and weakly-singular Green's functions used in the integral representations. Our method has immediate application to a variety of problems in computational physics. We concentrate here on studying its performance in acoustic scattering (governed by the Helmholtz equation) at low to moderate frequencies.

READ FULL TEXT
11/02/2022

A highly accurate perfectly-matched-layer boundary integral equation solver for acoustic layered-medium problems

Based on the perfectly matched layer (PML) technique, this paper develop...
09/29/2019

A fast boundary integral method for high-order multiscale mesh generation

In this work we present an algorithm to construct an infinitely differen...
07/03/2020

A fast direct solver for nonlocal operators in wavelet coordinates

In this article, we consider fast direct solvers for nonlocal operators....
07/16/2020

An alternative extended linear system for boundary value problems on locally perturbed geometries

This manuscript presents a new extended linear system for integral equat...
02/06/2021

Solving Fredholm second-kind integral equations with singular right-hand sides on non-smooth boundaries

A numerical scheme is presented for the solution of Fredholm second-kind...

Please sign up or login with your details

Forgot password? Click here to reset