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The goal of the GRUMMP project is to develop automatic mesh generation software for unstructured meshes with mixed element types. The software should produce high-quality meshes that meet user-defined mesh density requirements, using elements appropriate for the geometry and physics of a particular problem.
Automatic mesh generation for complex two and three dimensional domains is a topic of intensive research. It is imperative that automatic mesh generation tools be capable of generating quality finite element and finite volume meshes. There must be a balance between resolution of the boundary and surface features and complexity of the problem. In addition, for problems with isotropic physics, element aspect ratio must be small to minimize linear system condition number and interpolation error. On the other hand, problems with anisotropic physics (for example, a shear layer in viscous fluid flow) require highly anisotropic elements for efficient solution. A further level of complication is that for some physical problems and applications, quadrilateral (2D) or hexahedral (3D) elements are preferred, even though filling space with high quality elements is easier using triangular (2D) or tetrahedral (3D) elements.
A general-purpose automatic mesh generator should address all of these issues without excessive user intervention. We envision a system in which common types of physical problems have predefined mesh sizing and element aspect ratio functions, allowing easy generation of meshes for these applications areas. For flexibility and generality, the user will also be able to prescribe these functions (for totally different applications) or modify the predefined behaviors (to provide a quality mesh in the wake of an airplane wing, for example).
GRUMMP addresses these issues by implementing mesh manipulation primitives to generate of modify existing meshes so that criteria for element size and quality are met. In addition, automatic computation of local length scale is performed to provide a default in cases where solution-based adaptive length scales are not available.