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Conformal higher‐order remeshing schemes for implicitly defined interface problems
Author(s) -
Omerović Samir,
Fries ThomasPeter
Publication year - 2016
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5301
Subject(s) - polygon mesh , conformal map , convergence (economics) , boundary (topology) , finite element method , set (abstract data type) , interface (matter) , computer science , topology (electrical circuits) , algorithm , mesh generation , domain (mathematical analysis) , domain decomposition methods , mathematics , mathematical optimization , geometry , computational science , mathematical analysis , structural engineering , parallel computing , engineering , combinatorics , bubble , maximum bubble pressure method , economics , programming language , economic growth
Summary A new higher‐order accurate method is proposed that combines the advantages of the classical p ‐version of the FEM on body‐fitted meshes with embedded domain methods. A background mesh composed by higher‐order Lagrange elements is used. Boundaries and interfaces are described implicitly by the level set method and are within elements. In the elements cut by the boundaries or interfaces, an automatic decomposition into higher‐order accurate sub‐elements is realized. Therefore, the zero level sets are detected and meshed in a first step, which is called reconstruction. Then, based on the topological situation in the cut element, higher‐order sub‐elements are mapped to the two sides of the boundary or interface. The quality of the reconstruction and the mapping largely determines the properties of the resulting, automatically generated conforming mesh. It is found that optimal convergence rates are possible although the resulting sub‐elements are not always well‐shaped. Copyright © 2016 John Wiley & Sons, Ltd.