Metric Type in the Target-matrix Mesh Optimization Paradigm

Technical Report · Wed Dec 09 04:00:00 EST 2020

DOI:https://doi.org/10.2172/1782521· OSTI ID:1782521

Knupp, Patrick ^[1]

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1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

The Target Matrix Optimization Paradigm (TMOP) is a method for improving the accuracy, efficiency, and robustness of numerical solutions to partial differential equations by improving the geometric quality of the computational mesh, primarily through node movement. TMOP has been successfully applied to a number applications even though the paradigm was not fully understood at the time. With this work, TMOP can be seen to be a tightly woven fabric of interconnecting ideas and concepts that provides a powerful approach to mesh optimization. The central unifying concepts in TMOP are the concept of a Target Matrix and the concept of Metric Type. Target matrices are motivated by the desire to make mesh quality improvement application-specific and, when needed, solution-adaptive. Metric type plays an essential role because it provides, through the use of typed metrics, the bridge between application-specific quality and target construction. It is shown that there are eight theoretical metric types, including the shape and shape+size types used informally in the past. It is shown further that there exist well-posed metrics corresponding to six of the eight metric types. A well-posed metric is a metric that is typed and convex, polyconvex, or invex, and further, it is a metric that simplifies target construction.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• DOE Contract Number: AC52-07NA27344
• OSTI ID: 1782521
• Report Number(s): LLNL-TR-817490; 1027537
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING