The 4-triangles longest-side partition of triangles and linear refinement algorithms
Mathematics of Computation
A 3D refinement/derefinement algorithm for solving evolution problems
Applied Numerical Mathematics - Special issue on numerical grid generation-technologies for advanced simulations
Concrete Math
Mesh quality improvement and other properties in the four-triangles longest-edge partition
Computer Aided Geometric Design
The 8-tetrahedra longest-edge partition of right-type tetrahedra
Finite Elements in Analysis and Design
The propagation problem in longest-edge refinement
Finite Elements in Analysis and Design
The seven-triangle longest-side partition of triangles and mesh quality improvement
Finite Elements in Analysis and Design
Local refinement based on the 7-triangle longest-edge partition
Mathematics and Computers in Simulation
An overview of procedures for refining triangulations
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part I
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The triangle longest-edge bisection constitutes an efficient scheme for refining a mesh by reducing the obtuse triangles, since the largest interior angles are subdivided. One of these schemes is the four-triangle longest-edge (4T-LE) partition. Moreover, the four triangle self-similar (4T-SS) partition of an acute triangle yields four sub-triangles similar to the original one. In this paper we present a hybrid scheme combining the 4T-LE and the 4T-SS partitions which use the longest-edge based refinement. Numerical experiments illustrate improvement in angles and quality. The benefits of the algorithm suggest its use as an efficient tool for mesh refinement in the context of Finite Element computations.