## 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 N^{D},
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 SF_{6} 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) |

## Organisers

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