Stabilization by deflation for sparse dynamical systems without loss of sparsity

• 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.

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.