Meshless local Petrov–Galerkin (MLPG) method for wave propagation in 3D poroelastic solids

A meshless local Petrov–Galerkin (MLPG) method is applied to solve wave propagation problems of three-dimensional poroelastic solids with Biotʹs theory. The Laplace transform is used to eliminate the time dependence of the field variables for the transient elastodynamic case. A weak formulation with a unit step function transforms the set of governing equations into local integral equations on local subdomains. The meshless approximation based on the radial basis function (RBF) is employed for the implementation. Unknown Laplace-transformed quantities, including displacements of solid frame and pressure in the fluid, are computed from the local boundary integral equations. The time-dependent values are obtained by Durbinʹs inversion technique. In addition, a one-dimensional poroelasticity analytical solution is derived in this paper and introduced for comparison. Several numerical examples demonstrate the efficiency and accuracy of the proposed method.