Finite element approach to unbounded poisson and helmholtz problems using hybrid‐type infinite element

Abstract

AbstractElectric or sound field problems associated with an open boundary governed by a Poisson or Helmholtz equation, are analyzed via the finite element method in conjunction with a hybrid‐type infinite element. The original size and bandwidth of the system matrix of the finite region do not increase after connection of the infinite element matrices for expressing the outer infinite region. In this paper, errors associated with numerical calculations are examined for 3‐D fields in consideration of the infinite region. First, an infinite element matrix for 3‐D infinite acoustic field is derived. The formulations are easily applicable to the 3‐D electric field problems. Next, the numerical calculations are demonstrated for the acoustic field caused by a point driving source and the results are compared with the analytical solutions. Another numerical example is the calculation of electric field caused by a pair of electric charges. Reasonable accuracy is confirmed in the finite region, but the accuracy in the infinite region is not always satisfactory. The decay function used for the infinite element plays an important role in accuracy. The decay parameter can be determined by the aid of the minimum condition of the functional and it is found that the use of this condition promises reasonable results.