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Mixed Order Mesh Curving

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Mesh Generation and Adaptation

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 30))

Abstract

Linear hybrid unstructured meshes are elevated to mixed-order meshes in response to geometry curvature. The linear meshes are elevated to the required degree on an element-by-element basis in regions of high geometry curvature. Weighted condition number mesh smoothing is used to untangle and improve the quality of the current mixed-order mesh. Periodically the mesh is tested for additional element elevation using a deviation criterion. Once the mesh smoothing is complete the mesh can be exported as a mixed order mesh or uniformly elevated to the desired degree. Details of the mesh elevation and smoothing process are described. Two three-dimensional examples are included that demonstrate the effectiveness of the method to produce high quality mixed-order meshes.

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Notes

  1. 1.

    The intended application of this technique is mesh curving on NURB geometric surfaces but does not preclude use of discrete surfaces.

  2. 2.

    The highest surface and volume element degree will be Q4 even if the surface polynomial degree is higher.

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Correspondence to Carolyn D. Woeber .

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Karman, S.L., Karman-Shoemake, K., Woeber, C.D. (2022). Mixed Order Mesh Curving. In: Sevilla, R., Perotto, S., Morgan, K. (eds) Mesh Generation and Adaptation. SEMA SIMAI Springer Series, vol 30. Springer, Cham. https://doi.org/10.1007/978-3-030-92540-6_1

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