抛物边界积分算子的数据稀疏化 ACA 加速的混合插值方法

我们考虑抛物方程的边界积分 reformulation 的分段多项式不连续 Galerkin 离散化。 resulting linear systems are dense and block-lower triangular and hence can be solved by block forward elimination. For the fast evaluation of the history part, the matrix is subdivided into a family of sub-matrices according to the temporal separation. Separated blocks are approximated by Chebyshev interpolation of the heat kernel in time. For the spatial variable, we propose an adaptive cross approximation (ACA) framework to obtain a data-sparse approximation of the entire matrix. We analyse how the ACA tolerance must be adjusted to the temporal separation and present numerical results for a benchmark problem to confirm the theoretical estimates.