Computing density estimators with maximum a posteriori and sparse grids Locally adaptive greedy approximations for anisotropic parameter reduced basis spaces

We introduce a new fast numerical method for computing discontinuous solutions to the Boltzmann equation and illustrate it by numerical examples. A combination of adaptive grids for approximation of the distribution function and an approximate fast Fourier transform on non-uniform grids for computing smooth terms in the Boltzmann collision integral is used. 2008 Elsevier Inc. All rights reserved.

A new method for adaptive refinement of unstructured grids has been developed. This method ensures preservation of the element quality and the structural anisotropies of the initial grid. The flexibility of unstructured grids in combination with the implemented error estimation provides a powerful basis for three-dimensional simulation of tiine dependent processes.

The level set method, introduced by Osher and Sethian in 1988, is a powerful numerical approach for computing multi-phase flow problems. In 1994, Sussman, et al employed the level set approach to solve 2D incompressible two-phase flow problems. This approach was improved again by Sussman, et al in 1998. These methods are accurate but designed for structured uniform meshes only. In this paper, a...

Grid size (or resolution), when inadequate, can be an important source of uncertainty for air quality model (AQM) simulations. Coarse grids used because of computational limitations may artificially diffuse the emissions, leading to significant errors in the concentrations of pollutant species, especially those that are formed via non-linear chemical reactions. Further, coarse grids may result ...

In this paper, we present self-avoiding walks as a novel technique to \linearize" a triangular mesh. Unlike spacelling curves which are based on a geometric embedding, our algorithm is combinatorial since it uses the mesh connectivity only. We also show how the concept can be easily modi ed for adaptive grids that are generated in a hierarchical manner based on a set of simple rules, and made a...

A method for extracting intersection-free iso-surfaces from volumetric data with an octree structure is presented. Unlike contouring techniques designed for uniform grids (such as Marching Cubes), adaptive contouring methods (such as Dual Contouring) can and do often generate intersecting polygons. Our main contribution is a polygon generation algorithm that produces triangles enclosed in nonov...

Clustering is a key data mining problem. Density and grid based technique is a popular way to mine clusters in a large multi-dimensional space wherein clusters are regarded as dense regions than their surroundings. The attribute values and ranges of these attributes characterize the clusters. Fine grid sizes lead to a huge amount of computation while coarse grid sizes result in loss in quality ...