Numerical behavior of time domain BEM for three-dimensional transient elastodynamic problems

The present paper deals with the time domain formulation of the boundary element method for three-dimensional elastodynamic problems and its actual implementation for the solution of transient problems relative to bounded domains with any geometry. Particular attention is paid to stability and accuracy of the computed solutions. The numerical approach is based on a constant velocity prediction algorithm and the combination of the integral representation for several time steps. Quadratic boundary elements are considered. A subdivision of the elements is introduced for integration in order to preserve the causality condition and to improve the accuracy of the solution. As opposite to previously published techniques, the present approach is tested for finite 3D bodies with actual values of the elastic constants (non-zero Poisson's ratio). The obtained results show the stability and accuracy of the approach for a wide enough range of time step size and non-uniform meshes.

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