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FINITE ELEMENT SOLUTION OF A MODEL FREE SURFACE PROBLEM BY THE OPTIMAL SHAPE DESIGN APPROACH
Author(s) -
MEJAK GEORGE
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(19970430)40:8<1525::aid-nme127>3.0.co;2-s
Subject(s) - finite element method , discretization , mathematics , computation , algebraic equation , boundary value problem , mixed finite element method , surface (topology) , extended finite element method , numerical analysis , mathematical optimization , mathematical analysis , geometry , algorithm , engineering , physics , structural engineering , nonlinear system , quantum mechanics
Optimal shape design approach is applied to numerical computation of a model potential free boundary value problem. The problem is discretized using the finite element method. To test the approach the problem is formulated in both velocity potential and stream function formulation and four different finite element discretizations are used. Associated minimization problem is solved using the quasi‐Newton method. Gradient of the cost function is computed by solving the algebraic adjoint equation. Gravity and surface tension forces are included in the model. Viability of the method is showed by solving problems with important effects of gravity and surface tension forces. © 1997 by John Wiley & Sons, Ltd.