Special Wave Finite and Infinite Elements for Helmholtz Equation

摘要

This work deals with numerical modelling using special finite and infinite elements to solve Helmholtz equation efficiently. The approach is based on the partition of unity method. The potential at each node is expanded in a discrete series of approximating plane waves propagating in different directions so that the nodal shape functions are multiplied by trigonometric functions. Because of this choice of basis function a single finite element can contain many wavelengths, unlike conventional elements. The mesh model can thus remain unchanged even though the wave number increases. This approach greatly reduces the dimension of a problem for short waves in high frequency range.