A memory-efficient MultiVector Quasi-Newton method for black-box Fluid-Structure Interaction coupling

Abstract

In this work we present a novel Quasi-Newton technique for the black-box partitioned coupling of interface coupled problems. The new RandomiZed Multi-Vector Quasi-Newton method stems from the combination of the original Multi-Vector Quasi-Newton technique with the randomized Singular Value Decomposition algorithm, avoiding thus any dense DOFs-sized square matrix operation. This results in a reduction from quadratic to linear complexity in terms of the number of DOFs. Besides this, the need of storing the old inverse Jacobian is also avoided. Instead, only two very “thin” matrices are required to be saved, thus implying a much smaller memory footprint. Furthermore, our proposal can be used free of any user-defined parameter. The article describes the application of the method to the FSI interface residual equations in both Interface Quasi-Newton and Interface Block Quasi-Newton forms. For the latter, we also derive a closed form expression for the update, thus avoiding any linear system of equations resolution, by applying the Woodbury matrix identity to the inverse Jacobian decomposition matrices.