Section: New Results

From discrete to continuous metric fields

Participants : Patrick Laug [correspondant] , Houman Borouchaki.

Adaptive computation using adaptive meshes is now recognized as essential for solving complex PDE problems. This computation requires at each step the definition of a continuous metric field to govern the generation of the adapted meshes. In practice, via an appropriate a posteriori error estimation, metrics are calculated at the vertices of the computational domain mesh. In order to obtain a continuous metric field, the discrete field is interpolated in the whole domain mesh. In this study, a new method for interpolating discrete metric fields, based on a so-called “natural decomposition” of metrics, is introduced. The proposed method is based on known matrix decompositions and is computationally robust and efficient. Some qualitative comparisons with classical methods are made to show the relevance of this methodology [19] .