Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Set the sparse grid level to be used when peforming sparse grid integration or sparse grid interpolation
Alias: none
Argument(s): INTEGERLIST
Multidimensional integration by the Smolyak sparse grid method (specified with sparse_grid_level and, optionally, dimension_preference). The underlying onedimensional integration rules are the same as for the tensorproduct quadrature case; however, the default rule selection is nested for sparse grids (GenzKeister for normals/transformed normals and GaussPatterson for uniforms/transformed uniforms). This default can be overridden with an explicit non_nested specification (resulting in GaussHermite for normals/transformed normals and GaussLegendre for uniforms/transformed uniforms). As for tensor quadrature, the dimension_preference specification enables the use of anisotropic sparse grids (refer to the PCE description in the User's Manual for the anisotropic index set constraint definition). Similar to anisotropic tensor grids, the dimension with greatest preference will have resolution at the full sparse_grid_level and all other dimension resolutions will be reduced in proportion to their reduced preference. For PCE with either isotropic or anisotropic sparse grids, a summation of tensorproduct expansions is used, where each anisotropic tensorproduct quadrature rule underlying the sparse grid construction results in its own anisotropic tensorproduct expansion as described in case 1. These anisotropic tensorproduct expansions are summed into a sparse PCE using the standard Smolyak summation (again, refer to the User's Manual for additional details). As for quadrature_order, the sparse_grid_level specification admits an array input for enabling specification of multiple grid resolutions used by certain advanced solution methodologies.
This keyword can be used when using sparse grid integration to calculate PCE coefficients or when generating samples for sparse grid collocation.