document: H-matrix approximation for the operator exponential with applications We previously developed a data-sparse and accurate approximation to parabolic solution operators in the case of a rather general elliptic part given by a strongly P-positive operator . Also a class of matrices -LRB- H-matrices -RRB- has been analysed which are data-sparse and allow an approximate matrix arithmetic with almost linear complexity . In particular , the matrix-vector/matrix-matrix product with such matrices as well as the computation of the inverse have linear-logarithmic cost . In this paper , we apply the H-matrix techniques to approximate the exponent of an elliptic operator . Starting with the Dunford-Cauchy representation for the operator exponent , we then discretise the integral by the exponentially convergent quadrature rule involving a short sum of resolvents . The latter are approximated by the H-matrices . Our algorithm inherits a two-level parallelism with respect to both the computation of resolvents and the treatment of different time values . In the case of smooth data -LRB- coefficients , boundaries -RRB- , we prove the linear-logarithmic complexity of the method
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