Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Enhanced Relaxed Physical Factorization preconditioner for coupled
  poromechanics   The relaxed physical factorization (RPF) preconditioner is a recent algorithm
allowing for the efficient and robust solution to the block linear systems
arising from the three-field displacement-velocity-pressure formulation of
coupled poromechanics. For its application, however, it is necessary to invert
blocks with the algebraic form $\hat{C} = ( C + \beta F F^T)$, where $C$ is a
symmetric positive definite matrix, $FF^T$ a rank-deficient term, and $\beta$ a
real non-negative coefficient. The inversion of $\hat{C}$, performed in an
inexact way, can become unstable for large values of $\beta$, as it usually
occurs at some stages of a full poromechanical simulation. In this work, we
propose a family of algebraic techniques to stabilize the inexact solve with
$\hat{C}$. This strategy can prove useful in other problems as well where such
an issue might arise, such as augmented Lagrangian preconditioning techniques
for Navier-Stokes or incompressible elasticity. First, we introduce an
iterative scheme obtained by a natural splitting of matrix $\hat{C}$. Second,
we develop a technique based on the use of a proper projection operator
annihilating the near-kernel modes of $\hat{C}$. Both approaches give rise to a
novel class of preconditioners denoted as Enhanced RPF (ERPF). Effectiveness
and robustness of the proposed algorithms are demonstrated in both theoretical
benchmarks and real-world large-size applications, outperforming the native RPF
preconditioner.

11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ