New publication on an approximate block factorization preconditioner
31 Juli 2024
Our new article "An approximate block factorization preconditioner for mixed-dimensional beam-solid interaction" has been published as an open-access paper in the journal Computer Methods in Applied Mechanics and Engineering.
In this paper, we develop an approximate block factorization preconditioner tailored to the characteristics of the linear system arising in mixed-dimensional beam-solid interaction. Particular challenges arise due to the the penalty regularization of the coupling constraint as well as from the beam models themselves. After a block LU factorization, the beam sub-block of the system matrix is approximated by a Sparse Approximate Inverse (SPAI), which not only enables the explicit formation of a Schur complement, but also can be re-used in the predictor and corrector step of the block LU algorithm. Targeting a scalable solution process on parallel computing clusters, the inverse of the solid sub-block is approximated through algebraic multigrid (AMG). Numerical examples not only demonstrate weak scalability of the proposed preconditioner up to 1000 MPI ranks, but also demonstrate its superiority over existing solution methods in practical examples from civil engineering.
Firmbach, M., Steinbrecher, I., Popp, A., & Mayr, M. (2024). An approximate block factorization preconditioner for mixed-dimensional beam-solid interaction. In Computer Methods in Applied Mechanics and Engineering (Vol. 431, p. 117256). Elsevier BV. DOI (Open Access) 
