A Log-Barrier Method for Mesh Quality Improvement
Sastry, Shankar P., Suzanne M. Shontz and Stephen A. Vavasis
20th International Meshing Roundtable, Springer-Verlag, pp.329-346, October 23-26 2011
20th International Meshing Roundtable
October 23-26, 2011
Department of Computer Science and Engineering, The Pennsylvania State
University, University Park, PA, U.S.A., Department of Combinatorics and Optimization,
University of Waterloo, Waterloo, ON, Canada,
The presence of a few poor-quality mesh elements can negatively affect
the stability and efficiency of a finite element solver and the accuracy of the associated
partial differential equation solution. We propose a mesh quality improvement
method that improves the quality of the worst elements. Mesh quality improvement
of the worst elements can be formulated as a non-smooth unconstrained optimization
problem, which can be reformulated as a smooth constrained optimization problem.
Our technique solves the latter problem using a log-barrier interior point method
and uses the gradient of the objective function to efficiently converge to a stationary
point. The technique can be used with convex or non-convex quality metrics. The
method uses a logarithmic barrier function and performs global mesh quality improvement.
Our method usually yields better quality meshes than existing methods
for improvement of the worst quality elements, such as the active set, pattern search,
and multidirectional search mesh quality improvement methods.
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