Generic Algorithm for Meshing Arbitrary (Convex, Concave) Domain with Polygonal or Curved Boundaries by Quadrilateral Finite Elements

Syeda Sabikun Nahar (), Rina Paul () and Md. Shajedul Karim ()
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Syeda Sabikun Nahar: Aviation and Aerospace University, Bangladesh, Department of Science and Humanities
Rina Paul: Shahjalal University of Science and Technology, Department of Mathematics
Md. Shajedul Karim: Shahjalal University of Science and Technology, Department of Mathematics

SN Operations Research Forum, 2025, vol. 6, issue 4, 1-35

Abstract: Abstract Mesh generation is a special and pivotal task in the FEM solution process. The employment of lower-order (linear) quadrilateral finite elements often necessitates a greater number of elements than higher-order quadrilateral elements in meshing. FEM has two sorts of higher-order, namely Lagrange and serendipity-type quadrilateral elements. The use of such higher-order quadrilateral elements in meshing needs the use of an efficient algorithm. Furthermore, domain (convex, concave, or a combination of the two) discretization emphasizes the requirement for a generic approach. This article endeavors to present an efficient generic algorithm for meshing such domains (convex or concave) with (lower-, higher-order Lagrange, or serendipity-type) quadrilateral finite elements. First, we devise an algorithm to partition a given domain into a minimum number of convex subdomains, meshing each of them using (lower-, higher-order) quadrilaterals, and then further subdivide each quadrilateral into other quadrilaterals. This refining procedure continues until a fine mesh is formed. The algorithm requires only the type and order of the elements to mesh the domain with a polygonal boundary, whereas for meshing the domain with curved boundaries, equations of curves are also needed to be included in addition to the type and order of the elements. Then, after the final refinements, it prepares all elements’ data, e.g., node numbers, nodal coordinates, and connectivity of all quadrilaterals used in the mesh. Finally, for clarity and reference, the application of the algorithm is shown by meshing different domains using lower- and higher-order (Lagrange and serendipity type) quadrilateral elements. Highlights • Developed an efficient generic algorithm for meshing arbitrary domains. • The algorithm is suitable for meshing domain (convex, concave, and a combination of both) using higher-order serendipity as well as Lagrange-type quadrilateral elements. • The application of the algorithm substantiated by meshing different domains.

Keywords: Generic; Algorithm; Lagrange; Serendipity; Higher order; Quadrilaterals (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s43069-025-00532-y

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