Solution of Stokes flow in complex nonsmooth 2D geometries via a linear-scaling high-order adaptive integral equation scheme

08/30/2019
by   Bowei Wu, et al.
0

We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The key ingredient is a set of panel quadrature rules capable of evaluating weakly-singular, nearly-singular and hyper-singular integrals to high accuracy. Near-singular integral evaluation, in particular, is done using an extension of the scheme developed in J. Helsing and R. Ojala, J. Comput. Phys. 227 (2008) 2899--2921. The boundary of the given geometry is "panelized" automatically to achieve user-prescribed precision. We show that this adaptive panel refinement procedure works well in practice even in the case of complex geometries with large number of corners. In one example, for instance, a model 2D vascular network with 378 corners required less than 200K discretization points to obtain a 9-digit solution accuracy.

READ FULL TEXT

Authors

page 2

page 3

11/25/2021

Computing weakly singular and near-singular integrals in high-order boundary elements

We present algorithms for computing weakly singular and near-singular in...
02/11/2020

A robust solver for elliptic PDEs in 3D complex geometries

We develop a boundary integral equation solver for elliptic partial diff...
01/18/2022

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

We present a fast direct solver for boundary integral equations on compl...
05/26/2021

High-order close evaluation of Laplace layer potentials: A differential geometric approach

This paper presents a new approach for solving the close evaluation prob...
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...
06/03/2020

Fast multipole methods for evaluation of layer potentials with locally-corrected quadratures

While fast multipole methods (FMMs) are in widespread use for the rapid ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.