We consider the efficient solution of strongly elliptic partial differentialequations with random load based on the finite element method. The solution'stwo-point correlation can efficiently be approximated by means of an$\mathcal{H}$-matrix, in particular if the correlation length is rather shortor the correlation kernel is non-smooth. Since the inverses of the finiteelement matrices which correspond to the differential operator underconsideration can likewise efficiently be approximated in the$\mathcal{H}$-matrix format, we can solve the correspondent$\mathcal{H}$-matrix equation in essentially linear time by using the$\mathcal{H}$-matrix arithmetic. Numerical experiments for three-dimensionalfinite element discretizations for several correlation lengths and differentsmoothness are provided. They validate the presented method and demonstratethat the computation times do not increase for non-smooth or shortly correlateddata.
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