# C. JannaM3E · High Performance Computing

C. Janna

Associate Professor

Developing Chronos, a sparse linear algebra library for high performance computing

## About

97

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## Publications

Publications (97)

Algebraic multigrid (AMG) is one of the most widely used solution techniques for linear systems of equations arising from discretized partial differential equations. The popularity of AMG stems from its potential to solve linear systems in almost linear time, that is with an O(n) complexity, where n is the problem size. This capability is crucial a...

We develop a robust matrix-free, communication avoiding parallel, high-degree polynomial preconditioner for the Conjugate Gradient method for large and sparse symmetric positive definite linear systems. We discuss the selection of a scaling parameter aimed at avoiding unwanted clustering of eigenvalues of the preconditioned matrices at the extrema...

Frictional contact is one of the most challenging problems in computational mechanics. Typically, it is a tough non-linear 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...

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 i...

Modern engineering applications require the solution of linear systems of millions or even billions of equations. The solution of the linear system takes most of the simulation for large scale simulations, and represent the bottleneck in developing scientific and technical software. Usually, preconditioned iterative solvers are preferred because of...

Anthropogenic land subsidence can be evaluated and predicted by numerical models, which are often built over deterministic analyses. However, uncertainties and approximations are present, as in any other modeling activity of real-world phenomena. This study aims at combining data assimilation techniques with a physically-based numerical model of an...

A Correction to this paper has been published: https://doi.org/10.1007/s10596-021-10079-6

The solution of linear systems of equations is a central task in a number of scientific and engineering applications. In many cases the solution of linear systems may take most of the simulation time thus representing a major bottleneck in the further development of scientific and technical software. For large scale simulations, nowadays accounting...

The numerical simulation of the physical systems has become in recent years a fundamental tool to perform analyses and predictions in several application fields, spanning from industry to the academy. As far as large scale simulations are concerned, one of the most computationally expensive task is the solution of linear systems arising from the di...

The solution of linear systems of equations is a central task in a number of scientific and engineering applications. In many cases the solution of linear systems may take most of the simulation time thus representing a major bottleneck in the further development of scientific and technical software. For large scale simulations, nowadays accounting...

Underground Gas Storage (UGS) has become one of the most
widely used practices to cope with seasonal peaks in energy consumption. The
planning of any new UGS facility, or its upgrading to increase the working
gas volume and reservoir performance, must be supported by an evaluation of
possible induced effects on the environment. From a geomechanical...

Earth fissures accompanying anthropogenic land subsidence due to
excessive aquifer exploitation create significant geohazards in China.
Numerical models represent a unique scientific approach to predict the
generation and development of earth fissures. However, the common
geomechanical simulators fail to reproduce fissure development because they
c...

A critical issue concerning geomechanical safety for UGS (underground gas storage) in compartmentalized reservoirs is fault reactivation. Indeed, the displacement (land subsidence, land upheaval) and the stress fields caused by the seasonal injection and production of CH4 into and from deep reservoirs is peculiar. The need of improving our understa...

A 3D elasto‐plastic rate‐dependent model for rock mechanics is formulated and implemented into a Finite Element (FE) numerical code. The model is based on the approach proposed by Vermeer and Neher (A soft soil model that accounts for creep. In: Proceedings of the International Symposium “Beyond 2000 in Computational Geotechnics,” pages 249‐261, 19...

The reactivation of faults and the generation of fractures can be caused by stress changes due to injection and/or production of fluids into and/or from the subsurface. The simulation of these processes, which could be associated with (micro-)seismicity, is affected by a high uncertainty. The aim of this work is at developing a mathematical framewo...

The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size linear systems, especially when accurate results are sought for derived variables, like stress or deformation fields. Such a task represents the most time-consuming kernel, and motivates the development of robust and efficie...

This work discusses a general approach for preconditioning the block Jacobian matrix arising from the discretization and linearization of coupled multiphysics problem. The objective is to provide a fully algebraic framework that can be employed as a starting point for the development of specialized algorithms exploiting unique features of the speci...

The use of numerical models in geomechanics implicitly assumes a number of approximations and uncertainties, even though they are usually regarded as deterministic tools. Simplifications in the constitutive law, uncertainties in geomechanical parameters values, imposition of boundary conditions are only few examples of the probabilistic factors tha...

The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated with lower order functions, like stress or deformation fields. Such task represents the most time-consuming k...

The numerical simulation of structural mechanics applications via finite elements usually requires the solution of large-size and ill-conditioned linear systems, especially when accurate results are sought for derived variables interpolated with lower order functions, like stress or deformation fields. Such task represents the most time-consuming k...

The numerical simulation of modern engineering problems can easily incorporate millions or even billions degrees of freedom. In several applications, these simulations require the solution to sparse linear systems of equations, and algebraic multigrid (AMG) methods are often standard choices as iterative solvers or preconditioners. This happens due...

Biot’s equations of poroelasticity are numerically solved by an Element-based Finite Volume Method (EbFVM). A stabilization technique is advanced to avoid spurious pressure modes in the vicinity of undrained conditions. Classical benchmark problems and more realistic 3D test cases are addressed. The results show that the proposed stabilization is a...

One of the most time-consuming tasks in the procedures for the numerical study of PDEs is the solution to linear systems of equations. To that purpose, iterative solvers are viewed as a promising alternative to direct methods on high performance computers since, in theory, they are almost perfectly parallelizable. Their main drawback is the need of...

Initially observed in the semi-arid basins of southwestern USA, earth fissures due to aquifer over-exploitation are presently threatening a large number of subsiding basins in various countries worldwide. Different mechanics have been proposed to explain this process, such as differential compaction, horizontal movements, and fault reactivation. Nu...

The coupled equations of Biot's poroelasticity, consisting of stress equilibrium and fluid mass balance in deforming porous media, are numerically solved. The governing partial differential equations are discretized by an Element-based Finite Volume Method (EbFVM), which can be used in three dimensional unstructured grids composed of elements of di...

The use of factorized sparse approximate inverse (FSAI) preconditioners in a standard multilevel framework for symmetric positive definite (SPD) matrices may pose a number of issues as to the definiteness of the Schur complement at each level. The present work introduces a robust multilevel approach for SPD problems based on FSAI preconditioning, w...

Underground gas storage (UGS) is a practice that is becoming widely implemented to cope with seasonal peaks of gas consumption. When the target reservoir is located in a faulted basin, a major safety issue concerns the reactivation of pre-existing faults, possibly inducing (micro-) seismicity. Faults are reactivated when the shear stress exceeds th...

Factorized sparse approximate inverse (FSAI) preconditioners are robust algorithms for symmetric positive matrices, which are particularly attractive in a parallel computational environment because of their inherent and almost perfect scalability. Their parallel degree is even redundant with respect to the actual capabilities of the current computa...

In the numerical simulation of structural problems, a crucial aspect concern the solution of the linear system arising from the discretization of the governing equations. In fact, ill-conditioned system, related to an unfavorable eigenspectrum, are quite common in several engineering applications. In these cases the Preconditioned Conjugate Gradien...

Predicting the deformations of deep reservoirs due to fluid withdrawal/injection is a challenging task that could have important environmental, social, and economical impacts. Finite element models, if endowed with an appropriate constitutive law, represent a useful tool for computing the displacements, the deformations, and the stress distribution...

A numerical package called M3E_LINSOL for the solution of large linear systems of equations arising from reservoir simulations is presented. This suite includes Krylov-based solvers combined with a set of Factorized Sparse Approximate Inverse (FSAI) preconditioners specifically designed for massively parallel architectures. The computational effici...

The automatic generation of meshes for the Finite Element (FE) method can be an expensive computational burden, especially in structural problems with localized stress peaks. The use of meshless methods can address such an issue, as these techniques do not require the existence of an underlying connection among the particles selected in a general d...

Three dimensional numerical simulation of shallow tunnel excavation

The Jacobi–Davidson (JD) algorithm is considered one of the most efficient eigensolvers currently available for non-Hermitian problems. It can be viewed as a coupled inner-outer iteration, where the inner one expands the search subspace and the outer one reduces the eigenpair residual. One of the difficulties in the JD efficient use stems from the...

When large volumes of fluids are removed from or injected into underground formations for, e.g., hydrocarbon and water production, CO2 storage, gas storage, and geothermal energy exploitation, monitoring of surface deformations coupled to numerical modeling improves our understanding of reservoir behavior. The ability to accurately simulate surface...

Graphics Processing Units (GPUs) exhibit significantly higher peak performance than conventional CPUs. However, in general only highly parallel algorithms can exploit their potential. In this scenario, the iterative solution to sparse linear systems of equations could be carried out quite efficiently on a GPU as it requires only matrix-by-vector pr...

Krylov methods preconditioned by Factorized Sparse Approximate Inverses (FSAI) are an efficient approach for the solution of symmetric positive definite linear systems on massively parallel computers. However, FSAI often suffers from a high set-up cost, especially in ill-conditioned problems. In this communication we propose a novel algorithm for t...

The stress variation induced by aquifer overdraft in sedimentary basins with
shallow bedrock may cause rupture in the form of pre-existing fault
activation or earth fissure generation. The process is causing major
detrimental effects on a many areas in China and Mexico. Ruptures yield
discontinuity in both displacement and stress field that classic...

The automatic generation of meshes for the Finite Element method can be an expensive computational burden, especially in structural problems with localized stress peaks. The use of meshless methods can address such an issue, as these techniques do not require the existence of an underlying connection among the nodes selected in a general domain. Ho...

The Factorized Sparse Approximate Inverse (FSAI) is an efficient technique for preconditioning parallel solvers of symmetric positive definite sparse linear systems. The key factor controlling FSAI efficiency is the identification of an appropriate nonzero pattern. Currently, several strategies have been proposed for building such a nonzero pattern...

In recent years the growing popularity of supercomputers has fostered the development of algorithms able to take advantage of the massive parallelism offered by multiple processors. Direct methods, though robust and computationally efficient, hardly exploit high degrees of parallelism. By contrast, Krylov methods preconditioned by Factored Sparse A...

Gas injection into the subsurface is becoming increasingly popular worldwide in connection with Underground Gas Storage (UGS) and CO2 sequestration (CCS) projects. Depleted oil/gas fields or saline aquifers are strategically used to cope with the growing demand of energy and the planned reduction of the greenhouse efflux into the atmosphere. Due to...

Adaptive Block FSAI (ABF) is a novel preconditioner which has proved efficient for the parallel solution of symmetric positive definite (SPD) linear systems and eigenproblems. A possible drawback stems from its reduced strong scalability, as the iteration count to converge for a given problem tends to grow with the number of processors used. The pr...

The efficient solution to nonsymmetric linear systems is still an open issue, especially on parallel computers. In this paper we generalize to the unsymmetric case the Block Factorized Sparse Approximate Inverse (Block FSAI) preconditioner which has already proved very effective on symmetric positive definite (SPD) problems. Block FSAI is a hybrid...

Gas injection into the subsurface is becoming increasingly popular worldwide in connection with Underground Gas Storage (UGS) and CO2 sequestration (CCS) projects. Depleted oil/gas fields or saline aquifers are strategically used to cope with the growing demand of energy and the planned reduction of the greenhouse efflux into the atmosphere. Due to...

The implementation of suitable carbon capture and storage (CCS) technologies is a mandatory requirement for reducing anthropogenic emissions of greenhouse gases (GHG) and obtaining a sustainable power generation from fossil fuels, especially coal. Carbon dioxide (CO2) sequestration within deep underground reservoirs is indicated as one of the most...

Knowledge of ground compressibility in unloading/reloading conditions is of paramount importance in several geomechanical processes, but its estimate is often affected by large uncertainties, especially for deep rocks. Satellite measurements of the land motion can help improve this information. The present study investigates the ground response due...

The possible influence of the well casing in reservoir-deformation measurements by the radioactive-marker technique (RMT) is investigated. The issue is quite important because RMT data may be used for a most-representative estimate of the in-situ vertical rock compressibility cM (i.e., a basic parameter to predict the land settlement caused by gas-...

Remote sensing techniques have been widely used in recent decades to
monitor earth surface displacements related to seismic faults,
volcanoes, landslides, aquifers, hydrocarbon fields. In particular,
advanced InSAR techniques, such as SqueeSAR™, have already
provided unique results thanks to both the extension of the area which
can be monitored by...

The efficient parallel solution to large sparse linear systems of equations Ax = b is a central issue in many numerical computations in science and engineering. Iterative methods based on Krylov subspaces are particularly attractive for parallel simulations provided that an effective preconditioner is available, and actually this is often the most...

Underground gas storage (UGS) and CO2 sequestration (CCS) are strategic practices to address the growing demand of energy and reduction of greenhouse gas emission. There is an interest from the energetic, economic, and environmental viewpoint to store as much gas as possible consistent with the requirement of a safe disposal. A transversely isotrop...

Adaptive block factorized sparse approximate inverse (FSAI) (ABF) is a novel algebraic preconditioner for the cost-effective parallel solution of symmetric positive definite linear systems. However, a main drawback stems from its reduced scalability, as the iteration count to convergence tends to grow when the number of processors increases. A doma...

Volumetric changes in reservoirs due to fluid extraction and injection can induce either subsidence or uplift which could trigger fault reactivation and threaten well integrity. Surface deformation monitoring can provide valuable constraints on the dynamic behaviour of a reservoir through time. Whatever the surveying technique, the detection of mil...

The choice of the preconditioner is a key factor to accelerate the convergence of eigensolvers for large-size sparse eigenproblems. Although incomplete factorizations with partial fill-in prove generally effective in sequential computations, the efficient preconditioning of parallel eigensolvers is still an open issue. The present paper describes t...

The efficient solution to non-symmetric linear systems is still an open
issue on parallel computers. In this short pa-per we generalize to the
non-symmetric case the Block Factorized Sparse Approximate Inverse
(BFSAI) preconditioner which has already proved very effective on
symmetric positive definite (SPD) problems. The proposed algorithm is
expe...

Constraint preconditioners have proved very efficient for the solution of ill-conditioned finite element (FE) coupled consolidation problems in a sequential computing environment. Their implementation on parallel computers, however, is not straightforward because of their inherent sequentiality. The present paper describes a novel parallel inexact...

Land subsidence and uplift due to the production/injection of fluids
from/into the subsurface have been widely observed worldwide over the
last decades and occur for a variety of purposes such as groundwater
pumping, aquifer system recharge, gas/oil field development, enhanced
oil recovery, geologic CO2 sequestration, underground gas storage and
wa...

The present paper investigates the performance of a shifted factorized sparse approximate inverse as a parallel preconditioner for the iterative solution to the linear systems arising in the finite element discretization of non‐linear groundwater flow models. The shift strategy is based on an inexpensive preconditioner update exploiting the structu...

Parallel computers are potentially very attractive for the implementation of large size geomechanical models. One of the main difficulties of parallelization, however, relies on the efficient solution of the frequently ill-conditioned algebraic system arising from the linearization of the discretized equilibrium equations. While very efficient prec...

Efficient ad hoc preconditioners are a key factor for a successful implementation of linear solvers in a parallel computing environment. The class of Factorized Sparse Approximate Inverses (FSAI), although originally developed for scalar machines, has proven extremely promising in multicore hardware. A recent evolution of FSAI is Block FSAI (BFSAI)...

It is widely recognized that fossil fuel power plants will continue to
play an important role in the energy supply for a large number of
countries in the decades to come. The implementation of suitable CCS
technologies is a mandatory requirement for abating the GHG emissions
into the atmosphere and obtaining a sustainable power generation from
foss...

Preconditioning is a key factor to accelerate the convergence of sparse eigensolvers. The present communication describes the acceleration of a parallel Jacobi‐Davidson algorithm by using Block FSAI (BFSAI) as a preconditioner for symmetric positive definite eigenproblems. BFSAI proves a robust and efficient preconditioner in a number of test cases...

The finite element (FE) solution of geomechanical problems in realistic settings raises a few numerical issues depending on the actual process addressed by the analysis. There are two basic problems where the linear solver efficiency may play a crucial role: 1. fully coupled consolidation and 2. faulted uncoupled consolidation. A class of general s...

Evaluation of the environmental impact of UGS projectsSet-up and calibration of a 3-D FE transversally isotropic geomechanical modelPSInSAR analysis to measure vertical/horizontal movements of the land surface

An adaptive algorithm is presented to generate automatically the nonzero pattern of the block factored sparse approximate inverse (BFSAI) preconditioner. It is demonstrated that in symmetric positive definite (SPD) problems BFSAI minimizes an upper bound to the Kaporin number of the preconditioned matrix. The mathematical structure of this bound su...

Contact mechanics can be addressed numerically by Finite Elements using either a penalty formulation or the Lagrange multipliers.
The penalty approach leads to a linearized symmetric positive definite system which can prove severely ill-conditioned, with
the iterative solution to large 3D problems requiring expensive preconditioners to accelerate,...