Abstract of Tucker Carrington

Nonproduct quadrature grids for solving the vibrational Schrödinger equation
The size of the quadrature grid required to compute potential matrix elements impedes solution of the vibrational Schrödinger equation if the potential does not have a simple form. This quadrature grid-size problem can make computing (ρ)vibrational spectra impossible even if the size of the basis used to construct the Hamiltonian matrix is itself manageable. Potential matrix elements are typically computed with a direct product Gauß quadrature whose grid size scales as ND, where N is the number of quadrature points per coordinate and D is the number of dimensions. In this talk we demonstrate that this problem can be mitigated by using a pruned basis set and a nonproduct Smolyak grid. The constituent 1D quadratures are designed for the weight functions important for vibrational calculations. For the SF6 stretch problem (D=6) we obtain accurate results with a grid that is more than two orders of magnitude smaller than the direct product Gauß grid. If D>6 we expect an even bigger reduction.
(joint work with Gustavo Avila)


Lars Grasedyck (MPI Leipzig, Germany)
Wolfgang Hackbusch (MPI Leipzig, Germany)
Boris Khoromskij (MPI Leipzig, Germany)