Automatic domain partitioning for quadrilateral meshing with line constraints

In this paper, we present an algorithm for partitioning any given 2D domain into regions suitable for quadrilateral meshing. It is able to preserve the symmetry of the domain if any, and can deal with inner boundaries and multidomain geometries. Moreover, this method keeps the number of singularities at the junctions of the regions to a minimum. Although each part of the domain, being four-sided, can be easily meshed using a structured method, we provide a meshing process that guarantees near perfect quality for most quadrilaterals of the resulting mesh. The partitioning stage is achieved by solving a PDE-constrained equation based on the geometric properties of the domain boundaries. An analysis of the generated mesh quality is provided at the end, showcasing that the meshes obtained through our algorithm are especially suitable for finite element methods.

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