Finite element and domain decomposition methods for acoustic scattering problems.

摘要

In this thesis, the design, analysis and implementation of new Finite Element Methods—FEM—is approached and new stabilized methods are presented: the Residual-Free Bubbles—RFB; a two-level RFB/FEM and a combined Bubble-GLS method.; In addition, as finite element methods are not suitable for unbounded problems, the development of a coupled approach—FEM/OSRC—On Surface Radiation Conditions—is introduced, based on the Bayliss-Turkel like conditions.; A novel domain decomposition—DD—method for the solution of large realistic engineering acoustic scattering problems resulting from FEM discretizations is developed in this thesis. This method is, in essence, an extension of the Finite Element Tearing and Interconnecting—FETI—method to indefinite and complex systems resulting from the FEM discretization of the correspondent exterior Helmholtz problem. This new approach is named FETI-H (after FETI-Helmholtz) and has unique characteristics regarding efficiency, robustness and numerical scalability.; Large-scale realistic numerical simulations of submarine-shaped scatterers highlight the performance, accuracy and reliability of the methods developed in this thesis.