A systematic strategy for simultaneous adaptive hp finite element mesh modification using nonlinear programming
✍ Scribed by Abani Patra; Ashish Gupta
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 735 KB
- Volume
- 190
- Category
- Article
- ISSN
- 0045-7825
No coin nor oath required. For personal study only.
✦ Synopsis
Adaptive re®nement usually involves re®ning or enriching a fraction of mesh elements by one level based on a cut-o 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 modi®es 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 re®nement 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 simpli®ed 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.