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Tensor product decomposition of Helmholtz potential

## Boris Khoromskij (MPI Leipzig)

Modern methods of tensor-product decomposition allow an efficient data-sparse approximation to integral and more general nonlocal operators in higher dimensions. Examples of such nonlocal mappings are classical volume potentials, solution operators of elliptic/parabolic BVPs, collision integrals from the deterministic Boltzmann equation as well as the convolution integrals from the Hartree-Fock and Ornstein-Zernike equations in electronic/molecular structure calculations.

We discuss the structured low tensor-rank approximation to function-related tensors based on the Tucker model. For a class of analytic functions the asymptotic complexity of such approximations can be estimated by *O(log*^{d}n + dn log^{q}n), where *N=n*^{d} is the discrete problem size. We consider the application to the classical Helmholtz potential in *3D*. Numerical results will be addressed.