A new addition theorem for the 3-D Navier-Lamé system and its application to the method of fundamental solutions
This provides a computational tool for collocation methods in elasticity, but the improvement is incremental for specialists in numerical methods.
The authors derived a new addition theorem for the fundamental solution of the 3D Navier-Lamé system, enabling efficient expansions using Bessel functions and scalar spherical harmonics. They demonstrated its effectiveness in the method of fundamental solutions for exterior domain problems.
We obtain a new addition theorem for the fundamental solution of the Navier-Lamé system in dimension 3 satisfying the Kupradze radiation conditions. This provides an expansion of this fundamental solution that involves only the evaluation of Bessel functions and scalar spherical harmonics. This is particularly useful in collocation numerical methods based on fundamental solutions, such as the boundary element method or the method of fundamental solutions. For this last method, we show its efficiency when approximating the Navier-Lamé system in exterior domains.