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Anisotropic mesh optimization and its application in adaptivity
Author(s) -
Buscaglia Gustavo C.,
Dari Enzo A.
Publication year - 1997
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/(sici)1097-0207(19971130)40:22<4119::aid-nme254>3.0.co;2-r
Subject(s) - polygon mesh , generality , metric (unit) , convergence (economics) , mathematical optimization , boundary (topology) , computer science , domain (mathematical analysis) , mathematics , algorithm , topology (electrical circuits) , geometry , mathematical analysis , engineering , operations management , combinatorics , economics , psychotherapist , economic growth , psychology
The construction of solution‐adapted meshes is addressed within an optimization framework. An approximation of the second spatial derivative of the solution is used to get a suitable metric in the computational domain. A mesh quality is proposed and optimized under this metric, accounting for both the shape and the size of the elements. For this purpose, a topological and geometrical mesh improvement method of high generality is introduced. It is shown that the adaptive algorithm that results recovers optimal convergence rates in singular problems, and that it captures boundary and internal layers in convection‐dominated problems. Several important implementation issues are discussed. © 1997 John Wiley & Sons, Ltd.