Speaker
Description
Multi-point constraints are essential in modeling various engineering problems, for example in the context of joints undergoing large rotations or coupling of different element types in finite element analysis. The master-slave elimination is an efficient method for the numerical treatment of the constraints because it reduces the dimension of the resulting linear system which is particularly advantageous when a large number of constraints have to be considered. However, the method requires an inversion of the submatrix of the constraint Jacobian. For nonlinear constraints, this inversion has to be performed at every single iteration step of the Newton-Raphson scheme [1]. Nevertheless, the method exhibits a reduced computational complexity compared to Lagrange multipliers and the penalty method. This is also the case if the analysis of redundant constraints and the identification of slave degrees of freedom are included [2].
The aim of this talk is to present a method for drastically increasing the computational efficiency of this already efficient method. It is based on the exploitation of the specific structure of the constraint Jabocian as it appears in typical engineering applications. The analysis of this structure is based on the identification of constraint clusters and their coupling types, which can be performed in a pre-processing step without significant computational effort. All matrix operations required for this calculation are performed using the CSR technique for storing sparse matrices, which is also particularly advantageous because all the matrices required for this are already stored in this format. The corresponding algorithms are shown and their implementation is verified by principle examples. Finally, the master-slave elimination is extended by the exploitation of the structure of the constraint Jabocian which reduces the computational costs. The speed-up of the improved master-slave elimination over the previous master-slave elimination as well as other constraint methods is demonstrated using numerical examples.
[1] Boungard, J. and Wackerfuß, J.: Master-slave elimination scheme for arbitrary smooth nonlinear multi-point constraints. In: Computational Mechanics, 74(5):955–992, 2024
[2] Boungard, J. and Wackerfuß, J.: Identification, elimination and handling of redundant nonlinear multi-point constraints. In preparation.
