Updating meshes on deforming domains

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The resulting optimization problem typically has many challenging features, which requires the development of specially tuned numerical solvers.The target-matrix paradigm seeks to incorporate within one theoretical framework as many mesh types and application classes as possible.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.By spanning all these applications with one optimization construct, we are able to quickly tailor effective quality improvement algorithms to new problems as they arise.

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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.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.These target-based quality metrics are used to build a global objective function (or a sequence of local objective functions) using the power-mean template.This usually defines a continuous, multivariable optimization problem for which local extrema are sought.

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