Over the last several decades, many mesh generation methods and a plethora of adaptive methods for solving differential equations have been developed. In this talk, we take a general approach for describing the mesh generation problem, which can be considered as being in some sense equivalent to determining a coordinate transformation between physical space and a computational space. Our description provides some new theoretical insights into precisely what is accomplished from mesh equidistribution (which is a standard adaptivity tool used in practice) and mesh alignment. We show how variational mesh generation algorithms, which have historically been the most common and important ones, can generally be compared using these mesh generation principles. Lastly, we relate these to a variety of moving mesh methods for solving time-dependent PDEs.
This is joint work with Weizhang Huang, Kansas University
- Computational Mathematics and Applications Seminar