A fast solver for the Stokes equations with distributed forces in complex geometries
Journal of Computational Physics
Vortex blob methods applied to interfacial motion
Journal of Computational Physics
A high-order 3D boundary integral equation solver for elliptic PDEs in smooth domains
Journal of Computational Physics
Locally-corrected spectral methods and overdetermined elliptic systems
Journal of Computational Physics
A kernel-free boundary integral method for elliptic boundary value problems
Journal of Computational Physics
On the evaluation of layer potentials close to their sources
Journal of Computational Physics
Locally corrected semi-Lagrangian methods for Stokes flow with moving elastic interfaces
Journal of Computational Physics
Boundary integral solutions of coupled Stokes and Darcy flows
Journal of Computational Physics
Stokes-Darcy boundary integral solutions using preconditioners
Journal of Computational Physics
Journal of Computational Physics
Accurate computation of Stokes flow driven by an open immersed interface
Journal of Computational Physics
Partially implicit motion of a sharp interface in Navier-Stokes flow
Journal of Computational Physics
A kernel-free boundary integral method for implicitly defined surfaces
Journal of Computational Physics
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We develop a method for computing a nearly singular integral, such as a double layer potential due to sources on a curve in the plane, evaluated at a point near the curve. The approach is to regularize the singularity and obtain a preliminary value from a standard quadrature rule. Then we add corrections for the errors due to smoothing and discretization, which are found by asymptotic analysis. We prove an error estimate for the corrected value, uniform with respect to the point of evaluation. One application is a simple method for solving the Dirichlet problem for Laplace's equation on a grid covering an irregular region in the plane, similar to an earlier method of A. Mayo [SIAM J. Sci. Statist. Comput., 6 (1985), pp. 144--157]. This approach could also be used to compute the pressure gradient due to a force on a moving boundary in an incompressible fluid. Computational examples are given for the double layer potential and for the Dirichlet problem.