PETSc-based Parallel Finite Element Analysis And Its Application To Braced Excavation

In this paper, extensive and deep research has been carried out on the parallelfinite element method under the environment of MPI cluster. Parallel library PETSc isused to solve linear systems for geotechnical problems, especially in excavationengineering. First, under the high performance computation platform, the MPI parallelenvironment and parallel library PETSc are integrated into GLEAVES, which is ageotechnical software package used for the finite element simulation. The linear systemis solved with PETSc. And then, based on the consolidation problems in geotechnicalengineering, performance evaluations are carried out in the parallel software.Large-scale numerical simulations of foundation excavation are presented. The mainresults and achievements are summarized as follows:(1) A parallel version of GLEAVES which is a geotechnical software package isimplemented. The MPI parallel environment and parallel library PETSc are integratedinto GLEAVES and the linear system is solved with PETSc. The validity of the parallelversion has been verified.(2) Based on the consolidation problems in geotechnical engineering, performanceevaluations are carried out in the parallel software. The properties of the coefficientmatrix and the source of ill-conditioning in the linear system of geotechnical problemsare studied. Performance evaluations on Krylov subspace methods and preconditionersare done under the parallel environment. It is find that GMRES solver has goodstability for both symmetric and nonsymmetric linear systems, BiCGSTAB solver isshown to be robust on nonsymmetric and ill-conditioned systems and CG solver iswidely recognized as the de facto standard method for the solution of symmetricpositive definite system. Based on these conclusions, ill-conditioning due to contrastsin stiffnesses in soil-only model is studied. The result indicates that in soil-onlyproblems, ordinary preconditioner can improve convergence dramatically. On the otherhand, the effect on ill-conditioning due to the coefficient of permeability in soil-water coupled problems is discussed. It is find that iteration count and the solving difficultyincrease with the decrease of the coefficient of permeability. Besides, two parallelsparse direct solvers are discussed compared with the iterative method. Finally,performance evaluations are made on a soil-water coupled case with nearly one millionof degrees of freedom.(3) Large-scale numerical simulations of foundation excavation are used by theparallel version of the software. The key point and difficult point of large-scaleproblems of excavations are discussed and the practical projects are analysed. One caseis a3D large-scale model in soil-only condition and the precondioner Jacobi isimplemented. The result indicates that Jacobi preconditioner performs well to soil-onlyproblems. Another case is a3D large-scale one with soil-water coupled problems andthe procedure for choosing iterative solver and preconditioner is introduced. It is findthat the combination of GMRES solver and Jacobi preconditioner is stable whensolving soil-water coupled problems.