$${\mathcal {H}}$$H-matrix Accelerated Second Moment Analysis for Potentials with Rough Correlation

We consider the efficient solution of partial differential equations for strongly elliptic operators with constant coefficients and stochastic Dirichlet data by the boundary integral equation method. The computation of the solution’s two-point correlation is well understood if the two-point correlation of the Dirichlet data is known and sufficiently smooth. Unfortunately, the problem becomes much more involved in case of roughly correlated data. We will show that the concept of the $${\mathcal {H}}$$H-matrix arithmetic provides a powerful tool to cope with this problem. By employing a parametric surface representation, we end up with an $${\mathcal {H}}$$H-matrix arithmetic based on balanced cluster trees. This considerably simplifies the implementation and improves the performance of the $${\mathcal {H}}$$H-matrix arithmetic. Numerical experiments are provided to validate and quantify the presented methods and algorithms.

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