Two‐Scale Boolean Galerkin Discretizations for Fredholm Integral Equations of the Second Kind

Abstract

In this paper, some two‐scale Boolean Galerkin discretizations are proposed and analyzed for a class of Fredholm integral equations of the second kind in multidimensions. It is shown by both theory and numerics that this type of multiscale discretization algorithm not only significantly reduces the number of degrees of freedom but also produces very accurate approximations.