Parallel Hybrid Algorithm for Three-Dimensional Elastic Wave Scattering in Steel Pipes

A parallel computational algorithm that models three-dimensional elastic wave scattering in an infinite pipe is introduced. The algorithm combines two procedures: a Wave Function Expansion (WFE) and a Finite Element Discretization (FED). The WFE represents a flawless unbounded region while the FED idealizes a bounded region containing the defects. Unknown amplitudes in the WFE are determined by imposing continuity between the two regions; they are then used to calculate the reflection and transmission coefficients. The inversion of a large stiffness matrix resulting from the FED has been overcome in the current formulation by sub-structuring the finite element mesh. The algorithm is implemented in Fortran 90™ on a shared-memory, parallel computing platform using OpenMP™ directives. The algorithm is validated against available numerical and experimental results. Agreement with previous three-dimensional results for a radial crack in a steel pipe and a two-dimensional hybrid model of an axisymmetric cracked, welded steel pipe are shown to be excellent. New results are presented for an inclined crack in a steel pipe as well as for a non-axisymmetric cracked welded steel pipe.