Algebraic multigrid methods for direct frequency response analyses in solid mechanics

Algebraic multigrid (AMG) methods have proven to be effective for solving the linear algebraic system of equations that arise from many classes of unstructured discretized elliptic PDEs. Standard AMG methods, however, are not suitable for shifted linear systems from elliptic PDEs, such as discretized Helmholtz operators, due to the indefiniteness of the system and the presence of low energy modes which are difficult for multigrid methods to resolve effectively. This paper investigates simple methods to adapt existing standard AMG methods to these shifted systems from direct frequency response analyses in solid mechanics.