Year of start/end
2016 / 2021
PDGP CODE
DIT.AD021.049.002
Activity
| Metodologie e tecniche d'ingagine: Based on the knowledge acquired, we next plan to consider a number of novel approaches aiming at understanding the level of control that PDE analysis requirements are allowed to cast on the tessellation. Recent results suggest that a segmentation of the domain to be tessellated may be the way to go and that understanding the structure and main features of the domain allows to reduce unnecessary singularities in the tessellation. We will pursue various directions of investigation for the automatic definition of base-complexes aligned with prominent structures of the domain and/or the solution of the PDE. Moreover, we wish to define a series of operations acting on the combinatorial complex underlying the tessellation to allow several types of splitting and agglomeration of elements. Local mesh quality optimization strategies will be devised: discrete exterior calculus will be the reference theoretical framework for developing suitable mesh quality metrics and for the evaluation of error estimators able not only to give information on which elements to cut, but also on how to cut them, by anisotropic information as Hessians, curvatures of iso-lines etc. |
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| Abstract: This subproject aims at setting the mathematical framework for defining a representation scheme supporting the construction and manipulation of analysis suitable polyhedral tessellations. More precisely we want to be able to somehow construct polyhedral tessellations of a domain, complying with quality criteria that might be dictated by the analysis side. On such tessellations our algorithm should be able to perform a number of operations: (i) cutting a polyhedron as union of polyhedra; (ii) agglomerating polyhedra to form a new polyhedron; (iii) locally modify a tessellation to improve its quality. We also would like the algorithm to be able to automatically select the "best" way, that is to cut (or agglomarate) in such a way that the resulting mesh "quality" (as defined by the user/PDE solver) is as good as possible. These operations make it quite natural to construct a hierarchy of tessellations to be possibly used in a multilevel approach, and the algorithms should be able to keep track of the (local) embedding of one mesh into another, so as to provide information which will allow the PDE solver to perform operations like restrictions and extensions. |
CNR (PDGP) Project
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Last update: Jul/2020