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Updating meshes on deforming domains

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.

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The target-matrix paradigm seeks to incorporate within one theoretical framework as many mesh types and application classes as possible.Many applications in computational science such as heat transfer, advectiondiffusion, and fluid dynamics numerically solve partial differential equations.To numerically solve the equations, finite element, finite volume, and other PDEdiscretization methods are commonly used, along with meshes to discretize the physical domain.Using Mesquite on an ALE computation in which a projectile dents a cylinder.The image on the left shows the results with the standard equipotential smoother, which fails at 38.0s.It is well-known that the mesh and its quality can greatly impact the accuracy of simulations, as well as solver efficiency [1], [2].

Mesh quality can be improved by various methods including adaptivity [3], [4], smoothing [5], [6], and swapping [7], [8].

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.

We used the deforming mesh metric to prototype geometry and mesh update model for potential use in SLAC National Accelerator Laboratory accelerator design studies.

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The key idea in the target-matrix paradigm is that one describes mesh quality in explicit rather than implicit terms, as has commonly been done in the past.