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A Practical Approach for Solving Mesh Optimization Problems using Newton's Method

Kim, Jibum, Rao V. Garimella, and Markus Berndt

Research Notes, 22nd International Meshing Roundtable, Springer-Verlag, pp.Research Note, October 13-16 2013

IMR
PROCEEDINGS

22nd International Meshing Roundtable
Orlando, FL
October 13-16, 2013

Incheon National University, Incheon, South Korea
Los Alamos National Laboratory, Los Alamos, NM, U.S.A.
Email: jibumkim@incheon.ac.kr, rao@lanl.gov, berndt@lanl.gov

Summary
We present a practical approach for solving volume and surface mesh optimization problems. Our approach is based on Newton's method which uses both first-order (gradient) and second-order (Hessian) derivatives of the non-linear objective function. The volume and surface optimization algorithms are modified such that surface constraints and mesh validity are satisfied. We also propose a simple and efficient Hessian modification method when the Hessian matrix is not positive definite. We demonstrate our approach by comparing our method with a popular nonlinear conjugate gradient method in terms of both efficiency and mesh quality.

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