An Iterative Domain Decomposition Method for the Solution of a Class of Indefinite Problems in Computational Structural Dynamics

The FETI-DP domain decomposition method (DDM) is extended to address the iterative solution of a class of indefinite problems of the form (A − σM)x = b, where A and M are two real symmetric positive semi-definite matrices arising from the finite element discretization of second-order elastodynamic problems, and σ is a positive number. A key component of this extension is a new coarse problem based on the free-space solutions of Navier’s homogeneous displacement equations of motion. These solutions are waves, and therefore the resulting DDM is reminiscent of the FETI-H method. For this reason, it is named here the FETI-DPH method. For a given σ, this method is numerically shown to be scalable with respect to all of the problem size, subdomain size, and number of subdomains. Its intrinsic CPU performance is illustrated for various ranges of σ with the solution on an Origin 3800 parallel processor of several large-scale structural dynamics problems.