Quadrature error estimates for layer potentials evaluated near curved surfaces in three dimensions

Quadrature over Curved Surfaces by Extrapolation

In this paper we describe and justify a method for integrating over curved surfaces. This method does not require that the Jacobian be known explicitly. This is a natural extension of extrapolation (or Romberg integration) for planar squares or triangles.

Error Estimates for Gauss Quadrature Formulas for Analytic Functions

1. Introduction. The estimation of quadrature errors for analytic functions has been considered by Davis and Rabinowitz [1]. An estimate for the error of the Gaussian quadrature formula for analytic functions was obtained by Davis [2]. McNamee [3] has also discussed the estimation of error of the Gauss-Legendre quadrature for analytic functions. Convergence of the Gaussian quadratures was discu...

Fast convolution quadrature for the wave equation in three dimensions

This work addresses the numerical solution of time-domain boundary integral equations arising from acoustic and electromagnetic scattering in three dimensions. The semidiscretization of the time-domain boundary integral equations by Runge-Kutta convolution quadrature leads to a lower triangular Toeplitz system of size N . This system can be solved recursively in an almost linear time (O(N logN)...

Asymptotic Error Estimates for the Gauss Quadrature Formula

Positively Curved Surfaces in the Three-sphere

In this talk I will discuss an example of the use of fully nonlinear parabolic flows to prove geometric results. I will emphasise the fact that there is a wide variety of geometric parabolic equations to choose from, and to get the best results it can be very important to choose the best flow. I will illustrate this in the setting of surfaces in a three-dimensional sphere. There are quite a few...