A Direct Smoothing Method For Surface Meshes

Proceedings, 8th International Meshing Roundtable, South Lake Tahoe, CA, U.S.A., pp.189-193, October 1999

MESHING
RESEARCH
CORNER

Abstract
Various algorithms employed in automated meshing of surfaces often produce distorted elements in the first phase. Different methods are used in the second phase to improve the quality of the mesh. Smoothing is one such method. In this method, the nodes are relocated without altering the element connectivity to improve the mesh quality. The most commonly used smoothing is called Laplacian smoothing. It is an iterative method. In this paper, a direct, method is presented for smoothing surface meshes. It is shown that a system of equations can be generated for the new nodal locations and then be solved for the constraints at once. The generation of the system of equations is very similar to assembling of global stiffness matrix from the element stiffness matrices. The element stiffness matrices are constant in local coordinate systems. In this method, final mesh is independent of the initial locations of unconstrained nodes.

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