A multi-frontal parallel algorithm for coupled thermo-hydro-mechanical analysis of deforming porous media

In this paper, a multi-frontal parallel algorithm is developed to solve fully coupled heat, water and gas ßow in deformable porous media. The mathematical model makes use of the modiÞed e¤ective stress concept together with the capillary pressure relationship and takes phase change and latent heat transfer into account. The chosen macroscopic Þeld variables are displacement, capillary pressure, gas pressure and temperature. The parallel program is developed on a cluster of workstations. The PVM (Parallel Virtual Machine) system is used to handle communications among networked workstations. The multi-frontal method has advantages such as numbering of the Þnite element mesh in an arbitrary manner, simple programming organization, smaller core requirements and shorter computation times. An implementation of this parallel method on workstations is discussed. The speedup and e¦ciency of this method is demonstrated and compared with a general domain decomposition method based on band matrix methods by numerical examples.