Download full text - ELSA - Europa

Treatment of links in partitioning (4)
• The Lagrange multipliers method (recall Part 1) may
be generalized as follows
• Synchronous case:
A = Cγ
m C
−1 T
Cv
= b
12
z = b−Cv n+ −Cγ
m −1
( f e − f
i )
Aλ = z
n
∆ t +∆t
γ =
2
• Asynchronous case: just replace the scalar γ by the
matrix:
old new
Γ= diag ( γ i
) δti
+ δtL
γ
i
=
2
• The connections matrix remains symmetric and
positive definite like in the synchronous case.
101
n+
1
Example 12a – Taylor bar impact revisited
• A - Solution with spatially uniform time increment
(BAMD01)
• B - Solution with space partitioning (BAMD03) 102
51