This paper presents a spectral boundary element formulation for analysis of structures subjected
to dynamic loading. Two types of spectral elements based on Lobatto polynomials and Legendre
polynomials are used. Two-dimensional analyses of elastic wave propagation in solids with and
without cracks are carried out in the Laplace frequency domain with both conventional BEM
and the spectral BEM. By imposing the requirement of the same level of accuracy, it was found
that the use of spectral elements, compared with conventional quadratic elements, reduced the
total number of nodes required for modeling high-frequency wave propagation. Benchmark
examples included a simple one-dimensional bar for which analytical solution is available and a
more complex crack problem where stress intensity factors were evaluated. Special crack tip
elements are developed for the ¯rst time for the spectral elements to accurately model the crack
tip ¯elds. Although more integration points were used for the integrals associated with spectral
elements than the conventional quadratic elements, shorter computation times were achieved
through the application of the spectral BEM. This indicates that the spectral BEM is a more
e±cient method for the numerical modeling of structural health monitoring (SHM) processes, in
which high-frequency waves are commonly used to detect damage, such as cracks, in structures.