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A minimization based mapping algorithm for data transfer between simulation meshes

Ein Algorithmus zur Datenübertragung zwischen Simulationsgittern mittels Minimierung
: Klimm, B.

Volltext urn:nbn:de:0011-n-959021 (2.5 MByte PDF)
MD5 Fingerprint: 6205c9171db00bc315cd35986b372df5
Erstellt am: 23.6.2009

Köln, 2009, 70 S.
Köln, Univ., Dipl.-Arb., 2009
Diplomarbeit, Elektronische Publikation
Fraunhofer SCAI ()
data transfer; mapping; finite element; interpolation; common refinement; simulation; mesh; grid; SCAIMapper; MpCCI; MapLib

Current numerical simulations of physical processes increasingly involve multiple disciplines and the use of two or more simulation codes operating on different meshes of the same physical domain. Those meshes can be finite element meshes with different element types and different fineness of discretization, and they can be geometrically non-matching even when modeling the same physical domain. Nevertheless, an accurate and physically conservative data transfer is needed to map simulation results between those meshes. Based on minimization, we present a data transfer scheme for finite element surface meshes that is inherently conservative and optimal in the L2 norm. For geometrically matching meshes we prove a first and second order accuracy in the discretization of the source and target mesh, respectively. Numerical experiments indicate even better convergence in the source discretization but confirm that the second order approximation in the target discretization is asymptotically tight. The method requires the integration of basis functions on a common refinement of source and target mesh. As the generation of such a common refinement is not trivial, we also discuss and test two variations of the method with inexact integration on either mesh. Integration on the source side is conservative but can lead to severe oscillations. The integration on the target side is no longer conservative, but generates good results for smooth functions. We evaluate the minimization method and its variations in different conceptional important examples as well as in practically relevant test cases and compare the results with a standard interpolation method. We can already recommend to use the method with source- or target-based integration in many applications. Theory and tests demonstrate that the common-refinement-based integration is superior in accuracy and conservation, but a robust implementation of this method is still in need and might be subject to future work.