A fast sparse grid based space-time boundary element method for the nonstationary heat equation
A fast algorithm that scales linearly in the number of degrees of freedom of the sparse tensor product space, is proposed. This fast sparse grid-based spatiotemporal boundary element method, is developed for the solution of the nonstationary heat equation. The thermal single layer potential is used as an indirect ansatz to provide a first kind integral equation, that is discretized by Galerkin's method with respect to the sparse tensor product of the spatial and temporal ansatz spaces. It is shown that the convergence rate is nearly the same as for the common Galerkin discretization. Finally, the H-matrix and Toeplitz structure of the resulting discretized operators are used to deliver the algorithm in a form able to compute the approximate solution in a complexity that essentially corresponds to that of the spatial discretization. A numerical example is implemented to illustrate the demonstrated theory.
scientific article; zbMATH DE number 6919808
scientific article