Block constrained versus generalized Jacobi preconditioners for iterative solution of large-scale Biots FEM equations
Generalized Jacobi (GJ) diagonal preconditioner coupled with symmetric quasi-minimal residual (SQMR) method has been demonstrated to be efficient for solving the 22 block linear system of equations arising from discretized Biots consolidation equations. However, one may further improve the performance by employing a more sophisticated non-diagonal preconditioner. This paper proposes to employ a block constrained preconditioner Pc that uses the same 22 block matrix but its (1,1) block is replaced by a diagonal approximation. Numerical results on a series of 3-D footing problems show that the SQMR method preconditioned by Pc is about 55% more efficient time-wise than the counterpart preconditioned by GJ when the problem size increases to about 180,000 degrees of freedom. Over the range of problem sizes studied, the Pc-preconditioned SQMR method incurs about 20% more memory than the GJ-preconditioned counterpart. The paper also addresses crucial computational and storage issues in constructing and storing Pc efficiently to achieve superior performance over GJ on the commonly available PC platforms.
generalized jacobi preconditioner symmetric quasi-minimal residual (sqmr) method biots consolidation equations block constrained preconditioner three-dimensional finite-element discretization