Higher order infinite elements for Helmholtz equation

Infinite elements have been successfully used to model situations where the domain of interest extends to infinity. The fundamental reason for using an infinite element is to approximate infinity for a bounded problem that extends to infinity and the same time conserve elements. Infinite elements are derived from standard finite elements and modified to represent a decay type behaviour as one or more dimensions approach infinity. This paper concerns a technique that the two mappings of the shape funtion and the integration rule can made identical. This leads to a new set of infinite defined higher order shape funtions and to retention of the finite element integration abscissae and weights. This paper has two novel features. First to solve wave problems by a Petrov-Galerkin method using new higher order infinite elements. The second feature is to give a design guide on the use of these infinite elements by solving the Helmholtz’s equation.