In the past the time domain solution of the wave equation has been limited to simplified problems. This was due to the limitations of analytical methods and the capacity of computers to manipulate and store 'large' blocks of spatial information. With the advent of 'super computers' the ability to solve such problems has significantly increased. This paper outlines a method for transient analysis of wave propagation in arbitrary domains using a boundary element method. The technique presented will allow the definition ofa domain, the input of impedance conditions on the domain's surface, the specification of inputs on the surface, and the specification of initial conditions within the domain. It will produce a complete solution of the wave equation inside the domain. The techniques are demonstrated using a program with a boundary element formulation of Kirchhoff s equation. The elements used are triangular and compatible. TNTRODUCTTON Numerical solution of time domain wave propagation studies is possible using a variety of techniques, including the generalized finite difference and finite element methods. However, there are certain advantages to using boundary integral methods since the complete spatial domain of interest need not be discretized. Furthermore, since a Green's function solution is inherent in the boundary integral formulation, some of the interpolation errors which are characteristic of both finite difference and finite element methods are avoided.
The original boundary integral time domain wave propagation formulations were developed by Cruse and Rizzo' and Cruse2 to study stress wave propagation in arbitrary domains. The technique solved the integral equations in the Laplace domain and then inverse transformed the solution to obtain the time domain solution. Reference 3 is a more recent work by Rizzo et al., on the three-dimensional treatment of elastic waves in frequency domain. Manolis and Beskos4 numerically solved the formulation of Cruse and Rizzo for two-dimensional dynamic stress concentration studies. This transformation technique requircs a large number of boundary integral evaluations in the Laplace domain in order that the time domain solution be accurate and have a large bandwidth. Thus, the Laplace transform-based techniques are relatively expensive, especially for three-dimensional problems.
Direct time domain solutions of scalar wave propagation have been developed by Mansur and