Solution of Equilibrium Equations in Static Analysis: LDLT Solution ...

Efficiency of the solution
•form K = i – m i , for all i > m K (i.e. for constant column height): LDL T
decomposition requires n[m K + (m K ‐1)+ … +1] = ½ nm K2 operations,
reduction and backsubstitution of a load vector requires 2nm K operations
•in general (without constant column height): for decomposition of K and
reductionand backsubstitutionof R we get total of ½ Σ(i –m i ) 2 + 2 Σ(i –m i )
operations
• number of operations is governed by the pattern of nonzero elements in
thematrix ti
15-Jun-07
Method of Finite Elements I
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