Seminar in Numerical Analysis: Jürgen Dölz (Universität Bonn)

An evolutionary, fast, and oblivious compression approach to Volterra integral operators

We propose an efficient algorithm for the treatment of Volterra integral operators based on H2-matrix compression techniques. The algorithm is built in an evolutionary manner, and therefore, is well suited for the problems, where the right hand side depends on the solution itself and is not known for all time steps a priori. The resulting algorithm is of linear complexity O(N) w.r.t. to the number of time steps, and requires O(N) active memory. The memory consumption can be reduced to O(log N) for the kernels of convolution type using the Laplace inversion techniques introduced by Lubich et al; the connection to the FOCQ algorithm is drawn. We demonstrate the effectiveness of our algorithm on a series of numerical examples.

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