Partitioned Solution Procedure for Simultaneous Integration of Coupled-Field Problems

Abstract

SUMMARYAn implicit unconditionally stable partitioned solution procedure for the simultaneous integration of transient coupled ®eld problems is presented. The procedure does not require that the full system of coupled equations be assembled, and allows use of existing single-®eld analysis software modules to solve the coupled ®eld problem. An iterative partitioned conjugate gradient procedure is used to avoid having to form and assemble the Schur complement matrix. The coupling matrices never need be formed, thus resulting in substantial computational savings.

A Parallelized 3D Geomechanical Solver for Fluid‐Induced Fault Slip in Poroelastic Media

“…The model is designed for HPC using the MPI library. This is the first time, in the literature, that the iterative partitioned CG approach introduced by [ 46 ] is applied to problems involving explicitly defined discontinuities, such as fractures and faults. The proposed finite-element implementation maintains the computational efficiency and modularity that Prevost [ 46 ] demonstrated for the continuous version of the solver.…”

“…The above term couples the velocity of normal fracture opening 𝜕 𝑤∕𝜕 𝑡 to pressure. After applying first-order time integration, assuming that the increment of hydraulic aperture Δ𝑤 is equal to the increment of normal fracture opening Δ𝛿 𝑛 , and substituting the finite element operators defined earlier, while eliminating the test function, we derive the displacement-to-pressure coupling product within the fracture: As outlined in the original work by [ 46 ], the global coupling matrices do not need to be directly constructed. Instead, 𝑨𝒑 -type products can be calculated at the level of integration points, integrated over the corresponding volume or area, and consequently aggregated into the relevant global vectors.…”

“…Furthermore, a specialized solver integrating two field equations has to be developed, hindering direct utilization of separate solvers specialized in pressure diffusion and static deformations. To overcome this obstacle, we solve the linear system by a partitioned iterative CG approach proposed by Prevost [ 46 ], who claimed it to be unconditionally stable, robust and computationally efficient for the simultaneous integration of transient coupled field problems.…”

“…The solver explicitly resolves both matrix and fractures. The algorithm follows the fully implicit iterative approach proposed by Prevost [ 46 ], allowing the independent use of mechanics and fluid flow solvers. This method ensures unconditional stability and robustness while maintaining computational efficiency in solving coupled field problems simultaneously.…”

Three dimensional simulation of fluid-driven frictional and tensile ruptures on existing discontinuities

“…In order to benefit from the hierarchical representation of the collocation boundary element matrix, we solve this Jacobian system of equations via an iterative method using a triangular block pre-conditioner. Such a preconditioning approach is very similar to the ones used for the solution of hydro-mechanical problems via finite element (see for examples Prevost (1997)…”