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A Guaranteed Quality Boundary Graded Triangular Meshing Algorithm Backed by a Computer-Assisted Proof

Xu, Jing and Audrey N. Chernikov

Research Notes, 22nd International Meshing Roundtable, Springer-Verlag, pp.Research Note, October 13-16 2013


22nd International Meshing Roundtable
Orlando, FL
October 13-16, 2013

Department of Computer Science, Old Dominion University, Norfolk, VA, U.S.A.
Email: {jxu,achernik}

The quality of mesh elements including shape and size influences the performance of finite elements analysis, interpolation, and contouring. The existence of small angles is especially critical for conditioning of the stiffness matrix in finite elements methods. In this paper we present a boundary graded triangular mesh generation algorithm that allows for guaranteed bounds on angles. Our proof program shows that our algorithm bounds the minimum angle above 5.65 degrees.

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