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Performance Optimization
• All examples seen so far used the same time increment
for all elements in the mesh.
∆t()
t
• May be penalizing in explicit
methods, especially in 3D when
mesh is locally very fine. The
smallest element drives the
calculation’s time increment.
• Alternative strategies where the step varies both in time
and in space: ∆t( xt , ).
– Spatial time step partitioning
– Domain decomposition
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Time Step Partitioning
• Due to J.P. Halleux (1985!)
• Time step is automatically varied in space
according to a binary partition (1, ½, ¼, etc.).
• Simple and elegant: activated by OPTI PART.
• Each element is integrated with a step much closer
to its stability limit than usual (better accuracy!)
• However, difficulties in B.C.s: any nodes subjected
to essential conditions are associated with the
deepest partition level (smallest step) at the moment.
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