1Blurb:: Level to use in sparse grid integration or interpolation 2 3Description:: 4 5Multi-dimensional integration by the Smolyak sparse grid method 6(specified with sparse_grid_level and, optionally, 7dimension_preference). The underlying one-dimensional integration 8rules are the same as for the tensor-product quadrature case; however, 9the default rule selection is nested for sparse grids (Genz-Keister 10for normals/transformed normals and Gauss-Patterson for 11uniforms/transformed uniforms). This default can be overridden with an 12explicit non_nested specification (resulting in Gauss-Hermite for 13normals/transformed normals and Gauss-Legendre for 14uniforms/transformed uniforms). As for tensor quadrature, the 15dimension_preference specification enables the use of anisotropic 16sparse grids (refer to the PCE description in the User's Manual for 17the anisotropic index set constraint definition). Similar to 18anisotropic tensor grids, the dimension with greatest preference will 19have resolution at the full sparse_grid_level and all other dimension 20resolutions will be reduced in proportion to their reduced 21preference. For PCE with either isotropic or anisotropic sparse grids, 22a summation of tensor-product expansions is used, where each 23anisotropic tensor-product quadrature rule underlying the sparse grid 24construction results in its own anisotropic tensor-product expansion 25as described in case 1. These anisotropic tensor-product expansions 26are summed into a sparse PCE using the standard Smolyak summation 27(again, refer to the User's Manual for additional details). As for 28quadrature_order, the sparse_grid_level specification admits an array 29input for enabling specification of multiple grid resolutions used by 30certain advanced solution methodologies. 31 32A corresponding sequence specification is documented at, e.g., 33\ref method-multifidelity_polynomial_chaos-sparse_grid_level_sequence and 34\ref method-multifidelity_stoch_collocation-sparse_grid_level_sequence 35 36 37Topics:: 38Examples:: 39Theory:: 40Faq:: 41See_Also:: 42method-multifidelity_polynomial_chaos-sparse_grid_level_sequence 43method-multifidelity_stoch_collocation-sparse_grid_level_sequence 44