Abstract
The accuracy and convergence of computational solutions of mesh-based methods is strongly dependent on the quality of the mesh used. We have developed methods for optimizing meshes that are comprised of elements of arbitrary polygonal and polyhedral type. We present in this research the development of r-h hybrid adaptive meshing technology tailored to application areas relevant to multi-physics modeling and simulation. Solution-based adaptation methods are used to reposition mesh nodes (r-adaptation) or to refine the mesh cells (h-adaptation) to minimize solution error. The numerical methods perform either the r-adaptive mesh optimization or the h-adaptive mesh refinement method on the initial isotropic or anisotropic meshes to maximize the equidistribution of a weighted geometric and/or solution function. We have successfully introduced r-h adaptivity to a least-squares method with spherical harmonics basis functions for the solution of the spherical shallow atmosphere model used in climate forecasting. In addition, application of this technology also covers a wide range of disciplines in computational sciences, most notably, time-dependent multi-physics, multi-scale modeling and simulation.