Development of a Class of Smoothness-Increasing- Accuracy-Conserving (SIAC) Methods for Post-Processing Discontinuous Galerkin Solutions.

摘要

Although discontinuous and continuous Galerkin methods have advantages mathematically and computationally, they suffer from one feature that can in turn become a disadvantage - they do not require high levels of smoothness at the element boundaries. Lack of smoothness across elements can hamper simulation post processing like feature extraction and visualization. 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. In particular, we propose to contribute both mathematically and algorithmically to the class of smoothness increasing and accuracy-conserving (SIAC) methods and to provide a robust and freely available software solution to the high-order simulation community.