Optimal local non-reflecting boundary conditions Original Research Article

A class of numerical methods to solve problems in unbounded domains is based on truncating the infinite domain via an artificial boundary β and applying some boundary condition on β, which is called a Non-Reflecting Boundary Condition (NRBC). In this paper a systematic way to derive optimal local NRBCs of given order is developed in various configurations. The optimality is in the sense that the local NRBC best approximates the exact nonlocal Dirichlet-to-Neumann (DtN) boundary condition for C∞ functions in the L2 norm. The optimal NRBC may be of low order but still represent high-order modes in the solution. It is shown that the previously derived localized DtN conditions are special cases of the new optimal conditions. The performance of the first-order optimal NRBC is demonstrated via numerical examples, in conjunction with the finite element method.