A systematic strategy for simultaneous adaptive hp finite element mesh modification using nonlinear programming

Adaptive refinement usually involves refining or enriching a fraction of mesh elements by one level based on a cut-off criterion, requiring several costly intermediate solutions before a mesh that yields an acceptable solution is obtained. We avoid this by formulating and solving the mesh design pro...

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Vydáno v:	Computer methods in applied mechanics and engineering Ročník 190; číslo 29; s. 3797 - 3818
Hlavní autoři:	Patra, Abani, Gupta, Ashish
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Amsterdam Elsevier B.V 13.04.2001 Elsevier
Témata:	Applied sciences Computational techniques Exact sciences and technology Finite-element and galerkin methods Mathematical methods in physics Mathematical programming Operational research and scientific management Operational research. Management science Physics Gradient Refinement method Irregularity Automatic mesh generation Adaptive method Optimization Finite element method Problem solving Convergence rate Nonlinear programming Program design Mesh generation Mathematical programming
ISSN:	0045-7825, 1879-2138
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Shrnutí:	Adaptive refinement usually involves refining or enriching a fraction of mesh elements by one level based on a cut-off criterion, requiring several costly intermediate solutions before a mesh that yields an acceptable solution is obtained. We avoid this by formulating and solving the mesh design problem as a mathematical program. Our approach simultaneously modifies both mesh size ( h) and local polynomial order ( p) to yield an “optimal” mesh for a target error or given computational cost with gradients from local convergence rates. Constraints such as the one irregularity rule during mesh refinement are systematically incorporated in this formulation. The design task leads to a mixed integer nonlinear program (MINLP), that is relaxed to an NLP. To reduce the computations for the NLP, we employ simplified analytical gradients derived from initial mesh calculations. Finally, we apply our method to three model problems showing that complex hp-adaptive grids can be obtained directly from a uniform coarse grid. A commercial optimization software, MINOS [B.A. Murtagh, M.A. Saunders, MINOS 5.4 User's Guide, Technical Report SOL 83-20R, Stanford University, Stanford, 1987, Revised February 1995], was used as the NLP optimizer.
Bibliografie:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0045-7825 1879-2138
DOI:	10.1016/S0045-7825(00)00298-X