Implicit monolithic parallel solution algorithm for seismic analysis of dam-reservoir systems

Özmen, Semih
This research mainly focuses on developing a computationally scalable and efficient solution algorithm that can handle linear dynamic analysis of dam-reservoir interaction problem. Lagrangian fluid finite elements are utilized and compressibility and viscosity of the fluid are taken into consideration during the reservoir modeling. In order to provide computational scalability and efficiency, domain decomposition methods implemented with parallel computing approaches such as Finite Element Tearing and Interconnecting (FETI) family solution algorithms are utilized for the coupling of the subdomains and a fully implicit monolithic solution algorithm is developed. Following that, the ways of performance improvements for the algorithm are demonstrated. Re-orthogonalization is utilized to increase the convergence rate of the solution of system equations and Krylov subspaces are utilized in order to decrease the required iterations for the future time integration steps. Additionally, utilization of deflation methods on Preconditioned Conjugate Gradient (PCG) and Finite Element Tearing and Interconnecting (FETI) family solvers is discussed. Due to the fact that efficiency and behavior of the deflation methods depends on the deflation vectors utilized, different deflation vector generation methods are also investigated. Two of the deflation vector generation methods are from literature, i.e. “Subdomain Deflation Method” and “Recursive Deflation Method for Heterogeneous Problems”. In addition to them, a novel semi-heuristic deflation vector generation strategy which relies on the pre-selected zero energy modes of finite element formulations is proposed. Requirements, improvements and efficiencies of these methods are demonstrated for the serial solution of water tank with flexible walls problem. In order to investigate the efficiency and scalability of the presented solution approach on the solutions of more realistic problems by computer clusters, this approach is implemented by utilizing C++ programming language and PETSc library. In this parallel implementation, FETI-DP solution algorithm is utilized with different deflation vector generation algorithms. The efficiency and the scalability of the parallel solution framework are discussed for different types of finite elements, for different partitioning approaches and for different number of processors. Finally, the solution performance is presented for a large actual dam model, Pine Flat Dam in California, USA.