**P. Bochev, N. Trask, P. Kuberry, and B. Paskaleva**

*Center for Computing Research, Sandia National Laboratories*

**ABSTRACT**: Generalized Moving Least-Squares (GMLS is an abstract non-parametric regression technique that allows one to approximate any bounded linear functional from scattered samples of its argument. While GMLS has its origins in classic scattered data approximation theory it can also be a surprisingly effective and versatile tool for scientific computing. In this talk I will present four different examples from recent projects at Sandia that illustrate the powers of GMLS. These include

- A Meshfree Mimetic Divergence operation that satisfies a discrete divergence theorem and can be used to construct a convervative meshfree (virtual) finite volume scheme;
- A hybrid Discontinuous Galerkin method that uses a poit cloud to define robust "shape" functions whose quality does not depend on the quality of the underlying mesh, which is used only to integrate the weak forms.
- A meshfree data transfer capability for native field representations in the Earth System Model, and
- A compact GMLS semiconductor device model for circuit design and analysis.

**Acknowlegments and disclaimer. **This material is based upon work supported by the U.S. Department of Energy, Office of Science Office of Advanced Scientific Computing Research under Award Number DE-SC-0000230927, and the Laboratory Directed Research and Development program at Sandia National Laboratories. This talk describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the talk do not necessarily represent the views of the U.S. Department of Energy or the United States Government.