R-Adaptive Mesh Quality Improvement

It has long been known that achieving accurate and efficient numerical solutions to PDE-based applications depends heavily on mesh quality. To improve the meshes generated as part of the TSTT project, we are developing a mesh quality improvement toolkit called MESQUITE. The primary aim of this project is to provide a freely available, comprehensive software package that would accommodate a number of different mesh element types, quality metrics, high-level solution strategies, and mesh optimization algorithms. We designed MESQUITE from the ground up in SciDAC-1, based on mesh quality improvement algorithms and software developed previously at SNL and ANL. MESQUITE Version 1.0 was released in mid-2005. We have assembled a team of TSTT/Mesquite researchers & developers including Michael Brewer (SNL), Lori Freitag (LLNL), Patrick Knupp (SNL), and Jason Kraftcheck (UW). MESQUITE was designed to be easily extensible in order to support new research in mesh quality improvement and to allow rapid delivery of prototype mesh optimization algorithms to applications. The use of classes such as MeshQualityMetric, ObjectiveFunction, QualityAssessor, TerminationCriterion, VertexMover, and InstructionQueue help us achieve an object-oriented, flexible design. Embedded within the various classes are member functions which perform the computationally intensive numerical calculations. These member functions avoid objects, use pointers, arrays, and other low-level data structures to ensure that the computations are as efficient as possible.

MESQUITE Version 1.0 does mesh untangling, element shape improvement, and deforming meshes on local mesh patches consisting of either triangular, tetrahedral, quadrilateral, hexahedral, or hybrid (including wedge and pyramid elements) unstructured meshes. The prototype has a number of state-of-the-art algorithms for optimization-based node point movement including steepest descent, conjugate gradient, feasible Newton, and active set solvers. In addition, considerable attention was given to the development of a flat mesh data structure for the internal representation of unstructured mesh data that is both highly efficient and convenient. To obtain our mesh data from the application and to provide interoperability, we use the TSTTM common mesh interface specification, upon which two important implementations, AOMD (RPI) and MDB (SNL), are based.

In SciDAC-1, Mesquite was (i) incorporated into the TSTT Shape Optimization service developed for the accelerator appplication, (ii) used to generate different geodesic meshes used to test various discretization methods for the CSU climate appliction, (iii) used in TSTT mesh generation programs (Cubit, Overture, NWGrid) in support of accelerators, biology, and other applications. Major customers of Mesquite in SciDAC-2 are expected to include accelerators, fusion, and biology. In anticipation of these applications, we are currently extending Mesquite capabilities, based on the Target Matrix paradigm, to perform (a) R-adaptive node-movement based on solution features & error estimates, (b) mesh alignment for plasma fusion simulations, (c) robust moving mesh algorithms for Shape Optimization and other applications, (d) quality improvement for meshes with high-order nodes, (d) faster optimization via improved optimization solvers (in cooperation with TOPS).

For a list of applications that have used Mesquite, plus additional information, see the Mesquite website.