oa 2D and 3D Simulation of Elastic Wave Propagation by Using Element Free Galerkin's Method

The element free Galerkin’s (EFG) technique is proposed for solving 2D and 3D elastic wave equation. In this paper, we compare the waveforms calculated by three methodologies; Finite Difference Method with 4th order accuracy in space (FDM4), traditional FEM and EFG. Traditional FEM and EFG are tested on two individual interpolating functions (IFUNC); 1st order (plane) IFUNC and 2nd order (curved) IFUNC. From the comparison to the exact waveforms of Lamb’s problem, the proposed algorism gives accurate waveforms. By two-dimensional implementation, FEM4 demonstrates more accurate result than traditional FEM with plane IFUNC and EFG with plane IFUNC demonstrates more accurate one than FEM4. However, by employing curved IFUNC, traditional FEM and EFG demonstrate almost same accuracy. Moreover, we expand 2D program to 3D one. On the case of 1st order (plane) interpolating function, EFG improves numerical accuracy of traditional FEM without the increase of computational memory.