Chemical Engineering Hand Written_Notes_Part_111

Chemical Engineering Hand Written_Notes_Part_111 - 224 5....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
224 5. OPTIMIZATION AND RELATED NUMERICAL SCHEMES f nding solution to above set of equations can be formulated as minimization of (10.11) min x Φ ( x ) The necessary condition for unconstrained optimality is (10.12) Φ ( x ) x = ∂F ( x ) x ¸ T F ( x )= 0 If we ignore the degenerate case where matrix ∂F ( x ) x ¸ is singular and vector F ( x ) belongs to null space of this matrix, the necessary condition for optimality is satis f ed when (10.13) F ( x )= 0 which also corresponds to the global minimum of Φ ( x ) . The Leverberg-Marquardt method is known to work well for solving optimization formulation of this type. 10.3. Finite Element Method for Solving ODE-BVP and PDEs [ 15, 16 ] . The f nite element method is a powerful tool for solving PDEs particularly when the system under consideration has complex geometry. This method is based on the optimization formulation. In this section, we provide a very brief introduction to the method of f nite element. 10.3.1.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 11/26/2011 for the course EGN 3840 taught by Professor Mr.shaw during the Fall '11 term at FSU.

Page1 / 2

Chemical Engineering Hand Written_Notes_Part_111 - 224 5....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online