Galerkin discretizations of integral operators in Rd require the efficient numerical evaluation of integrals I =∫S(1)∫S(2) f(x; y)dydx where S(1); S(2) are d-simplices and the integrand function f has a possibly nonintegrable singularity at x = y. In [A. Chernov, T. von Petersdorff, C. Schwab, Exponential convergence of hp quadrature for integral operators with Gevrey kernels, M2AN, 45(3):387{422, 2011] we constructed several families of ...

The goal of this paper is to establish exponential convergence of hp-version interior penalty (IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with piecewise analytic data in threedimensional polyhedral domains. More precisely, we shall analyze the convergence of the hp-IP dG methods considered in [30] which are based on !-geometric anisotropic ...

We address shape uncertainty quantification for the two-dimensional Helmholtz trans- mission problem, where the shape of the scatterer is the only source of uncertainty. In the framework of the so-called deterministic approach, we provide a high-dimensional parametrization for the interface. Each domain configuration is mapped to a nominal configuration, obtaining a problem on a fixed domain with stochastic coefficients. To compute surrogate ...