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Computational science and engineering within the Department of Energy (DOE) spans a wide variety of applications including accelerator design, fusion, climate, biology, combustion, nuclear reactors, and weapons design.Simulation codes for these applications typically solve complex sets of partial differential equations (PDEs) by employing discretization methods that convert the continuum PDE into a discrete system of equations defined on a grid or mesh.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.As a simple example, the quality of quadrilateral mesh elements is often measured against a square even though this is not always the proper choice when performing simulations.With target matrices, the reference element can take into account the need for specific element size, aspect ratio, and orientation, and how these must vary across the mesh.The same test problem run with the target matrix paradigm mesh smoothing methods runs t=60.0s.

Mathematically rigorous methods for formulating the smoothing problem entail the use of an objective function that measures quality; included in this category are the variational methods for structured meshes [9], [10], [11], and the direct optimization methods based on mesh entities such as lengths and angles [12], [13].You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version listed if standards is not an option).A general-purpose algorithm for mesh optimization via node-movement, known as the Target-Matrix Paradigm, is introduced.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.

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