Smoothness-Increasing Accuracy-Conserving (SIAC) Filters for Post-Processing Unstructured Discontinuous Galerkin Fields.

摘要

The purpose of this proposal is to develop smoothness-increasing accuracy-conserving filters that respect the mathematical properties of the data while providing levels of smoothness so that commonly used visualization tools can be used appropriately, accurately, and efficiently. The goals of this effort are to define, investigate, and address the technical obstacles inherent in visualization of data derived from high-order discontinuous Galerkin methods and to provide robust and easy to use algorithms to overcome the difficulties that arise due to lack of smoothness. The goal of this proposal is to construct smoothness-increasing accuracy-conserving (SIAC) filters for discontinuous Galerkin solutions on fully-unstructured triangular and tetrahedral meshes. In Particular, we propose to contribute both mathematically and algorithmically to the class of smoothness-increasing and accuracy-conserving (SIAC) methods to provide a robust and freely available software solution to the high-order simulation community.