Summary. 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 nonsmooth 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 nonconvex 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.
A computational methodology for simulating virtual inferior vena cava (IVC) filter placement and IVC hemodynamics was developed and demonstrated in two patient
We characterize the performance of gradientand Hessian-based optimization methods for mesh quality improvement. In particular, we consider the steepest descent and Polack-Ribière conjugate gradient methods which are gradient based. In the Hessian-based category, we consider the quasi-Newton, trust region, and feasible Newton methods. These techniques are used to improve the quality of a mesh by repositioning the vertices, where the overall mesh quality is measured by the sum of the squares of individual elements according to the aspect ratio metric. The effects of the desired degree of accuracy in the improved mesh, problem size, initial mesh configuration, and heterogeneity in element volume on the performance of the optimization solvers are characterized on a series of tetrahedral meshes.
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