关键词: 数值流形法, 无界域问题, 无限单元, 无限片, 线性水波问题

Abstract: Since its invention, the Numerical Manifold Method has been applied to the analysis of a wide variety of problems, including the analysis of structures, seepage flow, and crack propagation. These problems typically involve bounded domains, or interior problems. However, for problems such as underground and surface structures, wave propagation, and other unbounded domain problems or exterior problems, the behavior of field variables in the far field needs to be considered in the numerical solution process. In this study, we constructed a finite element cover and weight functions suited to unbounded domain problems using the Numerical Manifold Method. With consideration of the asymptotic behavior of field variables at infinity, a local approximation was constructed to approach the behavior of the infinite domain. Unlike the shape function of infinite elements in the finite element method, the weight function in our proposed method only needs to satisfy the partition of unity, while the local approximation needs to approximate the behavior of the field variables, which makes the approximation of field variables more reasonable. The results from numerical examples demonstrate that the proposed method is effective and yields accurate results with fewer elements.

Key words: numerical manifold method, unbounded domain problems, infinite elements, infinite patches, linear water wave problem