arXiv subjects

Massimiliano Ferronato

Publications and source records attributed to Massimiliano Ferronato.

13 recordsLinked to original sources

arXiv2026

A Stabilized Mortar Method for Discontinuities in Geological Media with Non-Conforming Grids

Accurate numerical simulation of fault and fracture mechanics is critical for the performance and safety assessment of many subsurface systems. The discretized representation of discontinuity surfaces and the robust simulation of their frictional contact behavior still represent major challenges. In this work, we use the mortar method to enforce the contact constraints and allow for non-conformity around the discontinuity surface, with a set of Lagrange multipliers playing the role of interface tractions. The formulation combines piecewise linear displacements with piecewise constant multipliers defined on one side of the fault interface (the non-mortar side). This choice for the Lagrange multipliers has a number of advantages from practical and computational viewpoints, but violates the inf-sup stability constraint. In order to stabilize the proposed formulation, we develop a traction-jump stabilization term to be added to the constraint equations. We use a macro-element analysis to derive an algorithmic strategy that automatically evaluates the proper scaling of the stabilization, without requiring any additional user-selected parameter. Numerical experiments demonstrate that the proposed formulation not only restores the inf-sup stability condition, but also recovers stable traction profiles in the presence of finer non-mortar sides, where other inf-sup-stable formulations fail. The proposed method is finally used to simulate non-linear contact conditions in non-conforming corner-point grids typically used in industrial geological applications.

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arXiv2026

Unexpected fault activation due to underground gas storage in produced reservoirs. Part I: Mathematical model and mechanisms

Underground gas storage (UGS) is a critical technology for managing seasonal gas consumption peaks, increasingly important in the face of market uncertainties. However, safety concerns arise when reactivating pre-existing faults in faulted basins, where human activities may trigger seismic events. Typically, faults are reactivated when shear stress exceeds a critical frictional threshold, but unexpected fault reactivations have been observed during cushion gas injection (CGI) and UGS cycles in the Netherlands, even when the stress regime suggests stability. This two-part study introduces a novel simulation framework to better understand the mechanisms behind fault reactivation in complex settings such as the Rotliegend formation in the Netherlands. A 3D mathematical model coupling frictional contact mechanics in faulted porous rocks with fluid flow allows for predictive analysis of fault behavior. The effect of the storage of different fluids for various purposes, such as the long-term sequestration of CO2, the regular injection and extraction cycles of CH4, and the highly irregular cycles of H2, is investigated with respect to fault activation hazard. The ultimate goal is to define a safe operational bandwidth for UGS activities in faulted reservoirs. Part I of this work presents this comprehensive simulation tool where a slip-weakening constitutive law is introduced to model fault behavior. The approach is designed to address the complex geological setting that characterizes the Rotliegend formation, where multiple factors influence the behavior of fault systems. We succeed in explaining and modeling the occurrence of unexpected fault reactivations. The analysis shows that reactivation during primary production (PP) causes stress redistribution, leading to a new deformed equilibrated configuration.

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arXiv2026

Unexpected fault activation due to underground gas storage in produced reservoirs. Part II: Definition of safe operational bandwidths

Underground gas storage is a versatile tool for managing energy resources and addressing pressing environmental concerns. While natural gas is stored in geological formations since the early 20th century, hydrogen has recently been considered as a potential candidate toward a more flexible and sustainable energy infrastructure. Furthermore, these formations can additionally capture gases that contribute to climate change, such as CO2. When such operations are implemented in faulted basins, however, safety concerns may arise due to the potential reactivation of pre-existing faults, which could trigger (micro)-seismicity events. In the Netherlands, it has been recently noted that fault reactivation can occur "unexpectedly" during the life of an underground gas storage (UGS) site, even when stress conditions are not expected to cause a failure. The present two-part work aims to develop a modeling framework to investigate the physical mechanisms causing such occurrences in previously produced gas reservoirs and define a safe operational bandwidth for pore pressure variation for UGS operations in the faulted reservoirs of the Upper Rotliegend Group, the Netherlands. This paper investigates in detail the mechanisms and crucial factors that result in fault reactivation at various stages of a UGS. The mathematical and numerical model described in Part I is used, also considering how the presence of stored gases may influence the mechanical properties of the reservoir and caprock, in particular the Young modulus. The study investigates the hazard of fault activation caused by the storage of different fluids for various purposes, such as long-term CO2 sequestration, CH4 and H2 injection and extraction cycles, and N2 injection as cushion gas. The results show how geological configuration, geomechanical properties, and reservoir operating conditions may increase the hazard of fault reactivation.

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arXiv2025

Triangular preconditioners for double saddle point linear systems arising in the mixed form of poroelasticity equations

In this paper, we study a class of inexact block triangular preconditioners for double saddle-point symmetric linear systems arising from the mixed finite element and mixed hybrid finite element discretization of Biot's poroelasticity equations. We develop a spectral analysis of the preconditioned matrix, showing that the complex eigenvalues lie in a circle of center $(1,0)$ and radius smaller than 1. In contrast, the real eigenvalues are described in terms of the roots of a third-degree polynomial with real coefficients. The results of numerical experiments are reported to show the quality of the theoretical bounds and illustrate the efficiency of the proposed preconditioners used with GMRES, especially in comparison with similar block diagonal preconditioning strategies along with the MINRES iteration.

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arXiv2025

A deep learning-based surrogate model for seismic data assimilation in fault activation modeling

Assessing the safety and environmental impacts of subsurface resource exploitation and management is critical and requires robust geomechanical modeling. However, uncertainties stemming from model assumptions, intrinsic variability of governing parameters, and data errors challenge the reliability of predictions. In the absence of direct measurements, inverse modeling and stochastic data assimilation methods can offer reliable solutions, but in complex and large-scale settings, the computational expense can become prohibitive. To address these challenges, this paper presents a deep learning-based surrogate model (SurMoDeL) designed for seismic data assimilation in fault activation modeling. The surrogate model leverages neural networks to provide simplified yet accurate representations of complex geophysical systems, enabling faster simulations and analyses essential for uncertainty quantification. The work proposes two different methods to integrate an understanding of fault behavior into the model, thereby enhancing the accuracy of its predictions. The application of the proxy model to integrate seismic data through effective data assimilation techniques efficiently constrains the uncertain parameters, thus bridging the gap between theoretical models and real-world observations.

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arXiv2025

A Physics-Informed Neural Network approach for compartmental epidemiological models

Compartmental models provide simple and efficient tools to analyze the relevant transmission processes during an outbreak, to produce short-term forecasts or transmission scenarios, and to assess the impact of vaccination campaigns. However, their calibration is not straightforward, since many factors contribute to the rapid change of the transmission dynamics during an epidemic. For example, there might be changes in the individual awareness, the imposition of non-pharmacological interventions and the emergence of new variants. As a consequence, model parameters such as the transmission rate are doomed to change in time, making their assessment more challenging. Here, we propose to use Physics-Informed Neural Networks (PINNs) to track the temporal changes in the model parameters and provide an estimate of the model state variables. PINNs recently gained attention in many engineering applications thanks to their ability to consider both the information from data (typically uncertain) and the governing equations of the system. The ability of PINNs to identify unknown model parameters makes them particularly suitable to solve ill-posed inverse problems, such as those arising in the application of epidemiological models. Here, we develop a reduced-split approach for the implementation of PINNs to estimate the temporal changes in the state variables and transmission rate of an epidemic based on the SIR model equation and infectious data. The main idea is to split the training first on the epidemiological data, and then on the residual of the system equations. The proposed method is applied to five synthetic test cases and two real scenarios reproducing the first months of the COVID-19 Italian pandemic. Our results show that the split implementation of PINNs outperforms the standard approach in terms of accuracy (up to one order of magnitude) and computational times (speed up of 20%).

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arXiv2024

A novel Mortar Method Integration using Radial Basis Functions

The growing availability of computational resources has significantly increased the interest of the scientific community in performing complex multi-physics and multi-domain simulations. However, the generation of appropriate computational grids for such problems often remains one of the main bottlenecks. The use of a domain partitioning with non-conforming grids is a possible solution, which, however, requires the development of robust and efficient inter-grid interpolation operators to transfer a scalar or a vector field from one domain to another. This work presents a novel approach for interpolating quantities across non-conforming meshes within the framework of the classical mortar method, where weak continuity conditions are enforced. The key contribution is the introduction of a novel strategy that uses mesh-free Radial Basis Function (RBF) interpolations to compute the mortar integral, offering a compelling alternative to traditional projection-based methods. We propose an efficient algorithm tailored for complex three-dimensional settings allowing for potentially significant savings in the overall computational cost and ease of implementation, with no detrimental effects on the numerical accuracy. The formulation, analysis, and validation of the proposed RBF-based algorithm is discussed with the aid of a set of numerical examples, demonstrating its effectiveness. Furthermore, the details of the implementation are discussed and a test case involving a complex geometry is presented, to illustrate the applicability and advantages of our approach in real-world problems.

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arXiv2023

Block constrained pressure residual preconditioning for two-phase flow in porous media by mixed hybrid finite elements

This work proposes an original preconditioner that couples the Constrained Pressure Residual (CPR) method with block preconditioning for the efficient solution of the linearized systems of equations arising from fully implicit multiphase flow models. This preconditioner, denoted as Block CPR (BCPR), is specifically designed for Lagrange multipliers-based flow models, such as those generated by Mixed Hybrid Finite Element (MHFE) approximations. An original MHFE-based formulation of the two-phase flow model is taken as a reference for the development of the BCPR preconditioner, in which the set of system unknowns comprises both element and face pressures, in addition to the cell saturations, resulting in a $3 \times 3$ block-structured Jacobian matrix with a $2 \times 2$ inner pressure problem. The CPR method is one of the most established techniques for reservoir simulations, but most research focused on solutions for Two-Point Flux Approximation (TPFA)-based discretizations that do not readily extend to our problem formulation. Therefore, we designed a dedicated two-stage strategy, inspired by the CPR algorithm, where a block preconditioner is used for the pressure part with the aim at exploiting the inner $2 \times 2$ structure. The proposed preconditioning framework is tested by an extensive experimentation, comprising both synthetic and realistic applications in Cartesian and non-Cartesian domains.

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arXiv2021

A scalable preconditioning framework for stabilized contact mechanics with hydraulically active fractures

A preconditioning framework for the coupled problem of frictional contact mechanics and fluid flow in the fracture network is presented. The porous medium is discretized using low-order continuous finite elements, with cell-centered Lagrange multipliers and pressure unknowns used to impose the constraints and solve the fluid flow in the fractures, respectively. This formulation does not require any interpolation between different fields, but is not uniformly inf-sup stable and requires a stabilization. For the resulting 3 x 3 block Jacobian matrix, we design scalable preconditioning strategies, based on the physically-informed block partitioning of the unknowns and state-of-the-art multigrid preconditioners. The key idea is to restrict the system to a single-physics problem, approximately solve it by an inner algebraic multigrid approach, and finally prolong it back to the fully-coupled problem. Two different techniques are presented, analyzed and compared by changing the ordering of the restrictions. Numerical results illustrate the algorithmic scalability, the impact of the relative number of fracture-based unknowns, and the performance on a real-world problem.

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arXiv2021

A Reverse Augmented Constraint preconditioner for Lagrange multiplier methods in contact mechanics

Frictional contact is one of the most challenging problems in computational mechanics. Typically, it is a tough nonlinear problem often requiring several Newton iterations to converge and causing troubles also in the solution to the related linear systems. When contact is modeled with the aid of Lagrange multipliers, the impenetrability condition is enforced exactly, but the associated Jacobian matrix is indefinite and needs a special treatment for a fast numerical solution. In this work, a constraint preconditioner is proposed where the primal Schur complement is computed after augmenting the zero block. The name Reverse is used in contrast to the traditional approach where only the structural block undergoes an augmentation. Besides being able to address problems characterized by singular structural blocks, often arising in contact mechanics, it is shown that the proposed approach is significantly cheaper than traditional constraint preconditioning for this class of problems and it is suitable for an efficient HPC implementation through the Chronos parallel package. Our conclusions are supported by several numerical experiments on mid- and large-size problems from various applications. The source files implementing the proposed algorithm are freely available on GitHub.

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arXiv2021

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 $\hat{C} = ( C + βF F^T)$, where $C$ is a symmetric positive definite matrix, $FF^T$ a rank-deficient term, and $β$ a real non-negative coefficient. The inversion of $\hat{C}$, performed in an inexact way, can become unstable for large values of $β$, 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.

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arXiv2020

A novel block non-symmetric preconditioner for mixed-hybrid finite-element-based flow simulations

In this work we propose a novel block preconditioner, labelled Explicit Decoupling Factor Approximation (EDFA), to accelerate the convergence of Krylov subspace solvers used to address the sequence of non-symmetric systems of linear equations originating from flow simulations in porous media. The flow model is discretized blending the Mixed Hybrid Finite Element (MHFE) method for Darcy's equation with the Finite Volume (FV) scheme for the mass conservation. The EDFA preconditioner is characterized by two features: the exploitation of the system matrix decoupling factors to recast the Schur complement and their inexact fully-parallel computation by means of restriction operators. We introduce two adaptive techniques aimed at building the restriction operators according to the properties of the system at hand. The proposed block preconditioner has been tested through an extensive experimentation on both synthetic and real-case applications, pointing out its robustness and computational efficiency.

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arXiv2020

Efficient solvers for hybridized three-field mixed finite element coupled poromechanics

We consider a mixed hybrid finite element formulation for coupled poromechanics. A stabilization strategy based on a macro-element approach is advanced to eliminate the spurious pressure modes appearing in undrained/incompressible conditions. The efficient solution of the stabilized mixed hybrid block system is addressed by developing a class of block triangular preconditioners based on a Schur-complement approximation strategy. Robustness, computational efficiency and scalability of the proposed approach are theoretically discussed and tested using challenging benchmark problems on massively parallel architectures.

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