SANDIA_SGMGG Sparse Grid Mixed Growth, Generalized Construction

SANDIA_SGMGG is a MATLAB library which contains some experimental code for the investigation of sparse grids constructed in a generalized fashion, in which the set of indices corresponding to a sparse grid is chosen in a generalized way, rather than being defined by a linear constraint.

The sparse grid is associated with a data structure, whose management is a significant part of the computation.

We assume we are working in a space of dimension ND. An index vector is a list of ND nonnegative integers, which represent the level of quadrature in each dimension. A single index vector can be used to construct a product rule.

A sparse grid can be thought of as a weighted summation of product rules; our represention of a sparse grid will then consist of a list of NI index vectors, which we can regard as an ND by NI array.

Not every collection of index vectors will be admissible. For our purposes, a collection of index vectors is admissible if each vector in the set is admissible. An index vector that is part of a collection is admissible if it is the 0 vector, or every vector formed by decrementing exactly one entry by 1 is an admissible vector in the set.

Here is an example of an admissible collection of index vectors in 2D:

```        (0,3)
(0,2) (1,2)
(0,1) (1,1)
(0,0) (1,0) (2,0) (3,0) (4,0)
```
For the 2D case, an index is admissible if every possible index below or to the left of it is also in the set.

Languages:

SANDIA_SGMGG is available in a C++ version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

SGMGA, a MATLAB library which creates sparse grids based on a mixture of 1D quadrature rules, allowing anisotropic weights for each dimension.

Reference:

1. Thomas Gerstner, Michael Griebel,
Computing,
Volume 71, Number 1, August 2003, pages 65-87.

Examples and Tests:

You can go up one level to the MATLAB source codes.

Last revised on 24 August 2011.