Stabilization by deflation for sparse dynamical systems without loss of sparsity. (March 2016) - Cazzani, Antonio; Ruge, Peter
Abstract: Multiple-input, multiple-output models for coupled systems in structural dynamics including unbounded domains, like soil or fluid, are characterized by sparse system-matrices and unstable parts in the whole set of solutions due to spurious modes. Spectral shifting with deflation can stabilize these unstable parts; however the originally sparse system-matrices become fully populated when this procedure is applied. This paper presents a special consecutive treatment of the deflated system without losing the numerical advantages from sparsity. The procedure starts with an LU -decomposition of the sparse undeflated system and continues with restricting the solution space with respect to deflation using the same LU -decomposition. An example from soil–structure interaction shows the benefits of this consecutive treatment. Abstract : Highlights: MIMO models for coupled systems including unbounded domains are characterized by sparse system-matrices and unstable parts in the whole set of solutions (due to spurious modes). Spectral shifting with deflation stabilizes unstable parts; but system-matrices become fully populated. A special consecutive treatment of the deflated system without losing the numerical advantages from sparsity is proposed. Procedure starts with LU decomposition of the sparse undeflated system and restricts the solution space with respect to deflation using the same LU decomposition. Example from soil–structure interaction shows the benefits of this treatment.