Finite Differences

Abstract

The version of the FEM described in Chapter 6 is probably the simplest one. The FEM used in the modern commercial FE codes, such as PLAXIS and ABAQUS, benefit from enormous variety of different formulations, element and shape function types. Similarly, there are many different ways to solve a boundary value problem using finite differences. The version of the FDM described in this Chapter follows the one used in FLAC (Fast Lagrangian Analysis of Continua)—the only commercial FD code with broad geotechnical applications. The two special features of this version are: (a) discretization using a non-rectangular mesh, and (b) dynamic approach to solution of static problems. Thanks to these features, this method: (a) is practically identical to the simple version of the FEM described in Chapter 6; (b) is more efficient in terms of computer memory and for solution of nonlinear problems.