A fast sparse grid based space-time boundary element method for the nonstationary heat equation

This article presents a fast sparse grid based space-time boundary element method for the solution of the nonstationary heat equation. We make an indirect ansatz based on the thermal single layer potential which yields a first kind integral equation.This integral equation is discretized by Galerkin’s method with respect to the sparse tensor product of the spatial and temporal ansatz spaces. By employing the $\mathcal{H}$-matrix and Toeplitz structure of the resulting discretized operators, we arrive at an algorithm which computes the approximate solution in a complexity that essentially corresponds to that of the spatial discretization. Nevertheless, the convergence rate is nearly the same as in case of a traditional discretization in full tensor product spaces.