22nd International Meshing Roundtable
October 13-16, 2013
Incheon National University, Incheon, South Korea
Los Alamos National Laboratory, Los Alamos, NM, U.S.A.
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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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