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Creators/Authors contains: "Stees, Mike"

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  1. ; (, Spectral and High Order Methods for Partial Differential Equations, Proceedings of ICOSAHOM 2018, Lecture Notes in Computational Science and Engineering, Springer)
    Sherwin, Spencer J.; Moxey, David; Peiró, Joaquim; null (Ed.)
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  2. ; ; (, Proceedings of the 28th International Meshing Roundtable)
    One challenge in the generation of high-order meshes is that mesh tangling can occur as a consequence of moving the new boundary nodes to the true curved boundary. In this paper, we propose a new optimization-based method that uses signed angles to untangle invalid second- and third-order triangular meshes. Our proposed method consists of two passes. In the first pass, we loop over each high-order interior edge node and minimize an objective function based on the signed angles of the pair of triangles that share the node. In the second pass, we loop over face nodes and move them to the mean of the high-order nodes of the triangle to which the face node belongs. We present several numerical examples in two dimensions with second- and third-order elements that demonstrate the capabilities of our method for untangling invalid meshes. 
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  3. ; (, Lecture notes in computational science and engineering)
    To achieve the full potential of high-order numerical methods for solving partial differential equations, the generation of a high-order mesh is required. One particular challenge in the generation of high-order meshes is avoiding invalid (tangled) elements that can occur as a result of moving the nodes from the low-order mesh that lie along the boundary to conform to the true curved boundary. In this paper, we propose a heuristic for correcting tangled second- and third-order meshes. For each interior edge, our method minimizes an objective function based on the unsigned angles of the pair of triangles that share the edge. We present several numerical examples in two dimensions with second- and third-order elements that demonstrate the capabilities of our method for untangling invalid meshes. 
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    Full Text Available