The numerical manifold method for harmonic wave propagation in unbounded domains

The numerical manifold method (NMM) has been applied successfully to a wide variety of problems, including time-independent exterior problems, where problem domains are unbounded. However, of the utmost interest and significance is the analysis of wave propagation in unbounded domains, which is still an open issue because it is far more difficult than time-independent exterior problems. This study aims to fill partly this gap from the prospective of NMM. A new type of infinite patches and the local approximations are designed to construct the Galerkin approximation that satisfies the asymptotic behavior of waves at infinite. Different from the infinite element technique in the finite element method (FEM), where the shape functions are required to satisfy not only the continuity between finite and infinite elements but also the attenuation behavior of solution while approaching infinite, the NMM is demonstrated more straightforward and elegant in the construction of the Galerkin approximation. Some examples in propagation of elastic wave and surface water wave are investigated to verify the accuracy and applicability of the proposed method.