Nick Wyman, Pointwise’s director of applied research, will be presenting the results of some recent work on sizing functions for tetrahedral meshes at next week’s Symposium on Trends in Unstructured Mesh Generation (aka MeshTrends).

Nick’s presentation, Element-Size Gradation in an Unstructured Tetrahedral Mesh Using Radial Basis Functions, was co-authored with his Pointwise colleagues Mike Jefferies, Steve Karman, and John Steinbrenner, and is scheduled for Monday 27 July at 11:20 a.m. in room Promenade B.

Example of a tet mesh with an imposed element sizing field.

The presentation’s abstract:

Generation of a constrained tetrahedral mesh with a prescribed element size gradation requires knowledge of the desired element size at discrete locations in the domain. User control of element size gradation is provided through the constraining surface mesh, optional primitive (curve and surface) shape sources, influence parameters, and a background mesh size. These user controls, while convenient and natural, are in a form difficult to translate to an arbitrary point in the domain. Furthermore, if the input is inconsistent, which is common in the authors’ experience, discontinuities in the desired element size field can be created leading to poor mesh quality. We propose a method for general interpolation of a user prescribed element size field which also minimizes the effect of inconsistent input. A method for defining and interpolating a target 3D element size field utilizing radial basis functions (RBF) will be described. The process begins with the conversion of the constraining surface mesh and optional primitive shape sources into an equivalent element size field represented by radial basis functions. In our method, each RBF provides local target element size using a linear distance function. Selection of a linear distance function for element size allows for natural definition of the input influence parameter also known as the element growth rate. Furthermore, an individual RBF is only effective within a distance defined by the background mesh size and the influence parameter. Each constraining surface point contributes an RBF formed from the local surface element size, the influence parameter, and the background mesh size. Our application utilizes non-uniform rational basis spline (NURBS) curves and surfaces for primitive shape definition. Target element size and influence parameters are assigned at parametric locations within the NURBS definition. A discrete tessellation of the NURBS shape is then created with each point generating an RBF. Finally, the desired element size at a discrete position is calculated from a blend of the effective RBFs in the region. Results from a variety of weighting schemes will be presented along with efficiency gains introduced through the use of oct-tree sorting of the RBFs.

MeshTrends is a symposium held annually in conjunction with the U.S. National Congress on Computational Mechanics. This year’s event is being held in beautiful San Diego, California.

If you’ll be at MeshTrends, don’t hesitate to meet Nick and ask him questions about this research.