Solving a Rational Eigenvalue Problem in Fluid-Structure Interaction

Solving Rational Eigenvalue Problems via Linearization

The rational eigenvalue problem is an emerging class of nonlinear eigenvalue problems arising from a variety of physical applications. In this paper, we propose a linearization-based method to solve the rational eigenvalue problem. The proposed method converts the rational eigenvalue problem into a well-studied linear eigenvalue problem, and meanwhile, exploits and preserves the structure and p...

A Projection Method for a Rational Eigenvalue Problem in Fluid-Structure Interaction

A Maxmin Principle for Nonlinear Eigenvalue Problems with Application to a Rational Spectral Problem in Fluid–solid Vibration

In this paper we prove a maxmin principle for nonlinear nonoverdamped eigenvalue problems corresponding to the characterization of Courant, Fischer and Weyl for linear eigenproblems. We apply it to locate eigenvalues of a rational spectral problem in fluid-solid interaction. Dedicated to Prof. Dr. Karel Rektorys on the occasion of his 80th birthday

Presenting a Modified SPH Algorithm for Numerical Studies of Fluid-Structure Interaction Problems

A modified Smoothed Particle Hydrodynamics (SPH) method is proposed for fluid-structure interaction (FSI) problems especially, in cases which FSI is combined with solid-rigid contacts. In current work, the modification of the utilized SPH concerns on removing the artificial viscosities and the artificial stresses (which such terms are commonly used to eliminate the effects of tensile and numeri...

Compact Rational Krylov Methods for Nonlinear Eigenvalue Problems

We propose a new uniform framework of Compact Rational Krylov (CORK) methods for solving large-scale nonlinear eigenvalue problems: A(λ)x = 0. For many years, linearizations are used for solving polynomial and rational eigenvalue problems. On the other hand, for the general nonlinear case, A(λ) can first be approximated by a (rational) matrix polynomial and then a convenient linearization is us...