Parallel Finite Element Method and Time Stepping Control for Non-Isothermal Poro-Elastic Problems

This work focuses on parallel finite element simulation of thermal hydraulic and mechanical (THM) coupled processes in porous media, which is a common phenomenon in geological applications such as nuclear waste repository and CO2 storage facilities. The Galerkin finite element method is applied to solve the derived partial differential equations. To deal with the coupling terms among the equations, the momentum equation is solved individually in a monolithic manner, and moreover their solving processes are incorporated into the solving processes of nonisothermal hydraulic equation and heat transport equation in a staggered manner. The computation task arising from the present method is intensive if the method is applied to model a real geological application. Therefore, we present a parallel finite element method and a time stepping method with PI (proportional and integral feedback) automatic control to improve the computation efficiency. For parallel computing, the domain decomposition method is unitized to partition both computation tasks of the equation assembly and the linear solve, and the establishment of a global system of equations is thoroughly avoided. Moreover, an object-oriented concept of sparse matrix and iterative linear solver for large scale parallel and sequential simulation is developed. By simulating a real application with THM coupled processes, we show that the present parallel finite element method works fine for both monolithic and staggered scheme within coupling iterations, and furthermore we show the efficiency of the present method by the speedup we have achieved in the simulation.

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