NUMERICAL-SIMULATION OF INTERFACE WAVES BY HIGH-ORDER SPECTRAL MODELING TECHNIQUES

Few problems in elastodynamics have a closed-form analytical solution. The others can be investigated with semianalytical methods, but in ge neral one is not sure whether these methods give reliable solutions. T he same happens with numerical techniques: for instance, finite differ ence methods solve, in principle, any complex problem, including those with arbitrary inhomogeneities and boundary conditions. However, ther e is no way to verify the quantitative correctness of the solutions. T he major problems are stability with respect to material properties, n umerical dispersion, and the treatment of boundary conditions. In prac tice, these problems may produce inaccurate solutions. In this paper, the study of complex problems with two different numerical grid techni ques in order to cross-check the solutions is proposed. Interface wave s, in particular, are emphasized, since they pose the major difficulti es due to the need to implement boundary conditions. The first method is based on global differential operators where the solution is expand ed in terms of the Fourier basis and Chebyshev polynomials, while the second is the spectral element method, an extension of the finite elem ent method that uses Chebyshev polynomials as interpolating functions. Both methods have spectral accuracy up to approximately the Nyquist w ave number of the grid. Moreover, both methods implement the boundary conditions in a natural way, particularly the spectral element algorit hm. We first solve Lamb's problem and compare numerical and analytical solutions; then, the problem of dispersed Rayleigh waves, and finally , the two-quarter space problem. We show that the modeling algorithms correctly reproduce the analytical solutions and yield a perfect match ing when these solutions do not exist. The combined modeling technique s provide a powerful tool for solving complex problems in elastodynami cs.