Luca Formaggia

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Verified

Luca verified their affiliation via an institutional email.

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• Msc in mechanical engineering, Phd in numerical methods for engineering
• Professor (Full) at Politecnico di Milano

The full revised paper is now available at http://dx.doi.org/10.1016/j.cma.2017.03.039 The present work proposes a novel method for the simulation of crack propagation in brittle elastic materials that combines two of the most popular approaches in literature. A large scale displacement solution is obtained with the well known extended finite elem...

The process by which rocks are formed from the burial of a fresh sediment involves the coupled effects of mechanical compaction and geochemical reactions. Both of them affect the porosity and permeability of the rock and, in particular, geochemical reactions can significantly alter them, since dissolution and precipitation processes may cause a str...

In this work we discuss the reliability of the coupling among three-dimensional (3D) and one-dimensional (1D) models that describe blood flowing into the circulatory tree. In particular , we study the physical consistency of the 1D model with respect to the 3D one. To this aim, we introduce a general criterion based on energy balance for the proper...

Mesh adaptation on surfaces demands particular care due to the important role played by the surface fitting. We propose an adaptive procedure based on a new error analysis which combines a rigorous anisotropic estimator for the L1-norm of the interpolation error with an anisotropic heuristic control of the geometric error. We resort to a metric-bas...

The development of subsurface exploitation projects, including CO2 storage processes, requires a large number of numerical simulations where fluid and transport in porous media are coupled, at a certain stage, with the solution of the Biot problem, for instance, to evaluate the potential of faults destabilization and associated induced seismicity....

In this work, we present a comprehensive framework for the generation and efficient management of particles in both fully three-dimensional (3D) and depth-averaged Material Point Method (DAMPM) simulations. Our approach leverages TIFF image data to construct initial conditions for large-scale geophysical flows, with a primary focus on landslide mod...

Landslides are among the most dangerous natural disasters, with their unpredictability and potential for catastrophic human and economic losses exacerbated by climate change. Continuous monitoring and precise modeling of landslide-prone areas are crucial for effective risk management and mitigation. This study explores two distinct numerical simula...

Simulating the flow of two fluid phases in porous media is a challenging task, especially when fractures are included in the simulation. Fractures may have highly heterogeneous properties compared to the surrounding rock matrix, significantly affecting fluid flow, and at the same time hydraulic apertures that are much smaller than any other charact...

Our research is positioned within the framework of subsurface resource utilization for sustainable economies. We concentrate on modeling the underground single-phase fluid flow affected by geological faults using numerical simulations. The study of such flows is characterized by strong uncertainites in the data defing the problem due to the difficu...

Simulating the flow of two fluid phases in porous media is a challenging task, especially when fractures are included in the simulation. Fractures may have highly heterogeneous properties compared to the surrounding rock matrix, significantly affecting fluid flow, and at the same time hydraulic aperture that are much smaller than any other characte...

We present a two-dimensional semi-conservative variant of the depth-averaged material point method (DAMPM) for modelling flow-like landslides. The mathematical model is given by the shallow water equations, derived from the depth-integration of the Navier-Stokes equations with the inclusion of an appropriate bed friction model and material rheology...

We consider a single-phase depth-averaged model for the numerical simulation of fast-moving landslides with the goal of constructing a well-balanced, yet scalable and efficient, second-order time-stepping algorithm. We apply a Strang splitting approach to distinguish between parabolic and hyperbolic problems. For the parabolic contribution, we adop...

Environmental signals, acquired, e.g., by remote sensing, often present large gaps of missing observations in space and time. In this work, we present an innovative approach to identify the main variability patterns, in space–time data, when data may be affected by complex missing data structures. We formalize the problem in the framework of functi...

We present a two-dimensional semi-conservative variant of the depth-averaged material point method (DAMPM) for modelling flow-like landslides. The mathematical model is given by the shallow water equations, derived from the depth-integration of the Navier-Stokes equations with the inclusion of an appropriate bed friction model and material rheology...

We propose a scalable well-balanced numerical method to efficiently solve a modified set of shallow water equations targeting the dynamics of lava flows. The governing equations are an extension of a depth-integrated model already available in the literature and proposed to model lava flows. Here, we consider the presence of vents that act as point...

In this work, we present a mixed‐dimensional mathematical model to obtain the electric potential and current density in direct current simulations when a thin liner is included in the modelled domain. The liner is used in landfill management to prevent leakage of leachate from the waste body into the underground and is made of a highly‐impermeable...

We introduce a new method to efficiently solve a variant of the Pitman-Le two-phase depth-integrated system of equations, for the simulation of a fast landslide consolidation process. In particular, in order to cope with the loss of hyperbolicity typical of this system, we generalize Pelanti's proposition for the Pitman-Le model to the case of a no...

We investigate some computational aspects of an innovative class of PDEregularized statistical models: Spatial Regression with Partial Differential Equation regularization (SR-PDE). These physics-informed regression methods can account for the physics of the underlying phenomena and handle data observed over spatial domains with nontrivial shapes,...

In this work we present a mixed-dimensional mathematical model to obtain the electric potential and current density in direct current simulations when a thin liner is included in the modelled domain. The liner is used in landfill management to prevent leakage of leachate from the waste body into the underground and is made of a highly-impermeable h...

We consider a single phase depth-averaged model for the numerical simulation of fast-moving landslides with the goal of constructing a well-balanced positivity-preserving, yet scalable and efficient, second-order time-stepping algorithm. We apply a Strang splitting approach to distinguish between parabolic and hyperbolic problems. For the parabolic...

We propose a highly scalable solver for a two‐dimensional depth‐integrated fluid dynamic model in order to simulate flow‐like landslides, such as debris or mud flows. The governing equations are discretized on quadtree meshes by means of a two‐step second‐order Taylor‐Galerkin scheme, enriched by a suitable flux correction in order to avoid spuriou...

We present a novel model for fluid-driven fracture propagation in poro-elastic media. Our approach combines ideas from dimensionally reduced discrete fracture models with diffuse phase-field models. The main advantage of this combined approach is that the fracture geometry is always represented explicitly, while the propagation remains geometricall...

We propose a highly scalable solver for a two-dimensional depth-integrated fluid dynamic model in order to simulate flow-like landslides, such as debris or mud flows. The governing equations are discretized on quadtree meshes by means of a two-step second-order Taylor-Galerkin scheme, enriched by a suitable flux correction in order to avoid spuriou...

Mathematical models accounting of several space scales have proved to be very effective tools in the description and simulation of the cardiovascular system. In this chapter, we review the family of models that are based on partial differential equations defined on domains with hybrid dimension. Referring to the vascular applications, the most prom...

The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults, while the latter are connected to the properties of the rock matrix which might vary abruptly in space. The develo...

Recent advances in satellite technologies, statistical and mathematical models, and computational resources have paved the way for operational use of satellite data in monitoring and forecasting natural hazards. We present a review of the use of satellite data for Earth observation in the context of geohazards preventive monitoring and disaster eva...

In this work we present a formulation of Coulomb’s friction in a fractured elastic body as a PDE control problem where the observed quantity is the tangential stress across an internal interface, while the control parameter is the slip i.e. the displacement jump across the interface. The cost function aims at minimizing the norm of a non-linear and...

In this work, we address the problem of fluid-structure interaction (FSI) with moving structures that may come into contact. We propose a penalization contact algorithm implemented in an unfitted numerical framework designed to treat large displacements. In the proposed method, the fluid mesh is fixed and the structure meshes are superimposed to it...

This work deals with the efficient iterative solution of the system of equations stemming from mimetic finite difference discretization of a hybrid-dimensional mixed Darcy problem modeling flow in fractured porous media. We investigate the spectral properties of a mixed discrete formulation based on mimetic finite differences for flow in the bulk m...

An accurate modeling of reactive flows in fractured porous media is a key ingredient to obtain reliable numerical simulations of several industrial and environmental applications. For some values of the physical parameters we can observe the formation of a narrow region or layer around the fractures where chemical reactions are focused. Here, the t...

The last few years have witnessed a surge in the development and usage of discretization methods supporting general meshes in geoscience applications. The need for general polyhedral meshes in this context can arise in several situations, including the modelling of petroleum reservoirs and basins, CO2 and nuclear storage sites, etc. In the above an...

An accurate modeling of reactive flows in fractured porous media is a key ingredient to obtain reliable numerical simulations of several industrial and environmental applications. For some values of the physical parameters we can observe the formation of a narrow region or layer around the fractures where chemical reactions are focused. Here the tr...

In this work we present the mathematical models for single-phase flow in fractured porous media. An overview of the most common approaches is considered, which includes continuous fracture models and discrete fracture models. For the latter, we discuss strategies that are developed in literature for its numerical solution mainly related to the geom...

We present ADM-LTS, an adaptive multilevel space-time-stepping scheme for transport in heterogeneous porous media. At each time step, firstly, the flow (pressure) solution is obtained. Then, the transport equation is solved using the ADM-LTS method, which consists of two stages. In the first stage, an initial solution is obtained by imposing the co...

The numerical simulation of physical processes in the underground frequently entails challenges related to the geometry and/or data. The former are mainly due to the shape of sedimentary layers and the presence of fractures and faults, while the latter are connected to the properties of the rock matrix which might vary abruptly in space. The develo...

Some are rather old, so maybe are not working anymore on the latest versions of MATLAB. They are provided to readers of the Book without any warranties whatsoever. Not all exercises are covered. The book is available on Springer site (https://doi.org/10.1007/978-88-470-2412-0).

In this work, we address the problem of fluid-structure interaction with moving structures that may come into contact. We propose a penalization contact algorithm implemented in an unfitted numerical framework designed to treat large displacements. In the proposed method, the fluid mesh is fixed and the structure meshes are superimposed to it witho...

Accurate and efficient simulation of multiphase flow in heterogeneous porous media motivates the development of space-time multiscale strategies for the coupled nonlinear flow (pressure) and saturation transport equations. The flow equation entails heterogeneous high-resolution (fine-scale) coefficients and is global (elliptic or parabolic). The ti...

This volume collects state-of-the-art contributions on the numerical simulation of fractured porous media, focusing on flow and geomechanics. First appearing in issues of the International Journal on Geomathematics, these articles are now conveniently packaged in one volume. Of particular interest to readers will be the potential applications of mo...

This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the spatial domain. We propose a novel mass conservative multirate approach, that can be generalized to various im...

Plenary lecture given at the NUMTA19 Conference

This paper presents an algebraic dynamic multilevel method with local time-stepping (ADM-LTS) for transport equations of sequentially coupled flow in heterogeneous porous media. The method employs an adaptive multilevel space-time grid determined on the basis of two error estimators, one in time and one in space. More precisely, at each time step,...

This work deals with the efficient iterative solution of the system of equations stemming from mimetic finite difference discretization of a hybrid-dimensional mixed Darcy problem modeling flow in fractured porous media. We investigate the spectral properties of a mixed discrete formulation based on mimetic finite differences for flow in the bulk m...

Accurate and efficient simulation of multiphase flow in heterogeneous porous media motivates the development of space-time multiscale strategies for the coupled nonlinear flow (pressure) and saturation transport equations. The flow equation entails heterogeneous high-resolution (fine-scale) coefficients and is global (elliptic or parabolic). The ti...

In this work, we propose a model for the passive transport of a solute in a fractured porous medium, for which we develop a Hybrid High-Order (HHO) space discretization. We consider, for the sake of simplicity, the case where the flow problem is fully decoupled from the transport problem. The novel transmission conditions in our model mimic at the...

This works gives an overview of the mathematical treatment of state-of-the-art techniques for partial differential problems where boundary data are provided only in terms of averaged quantities. A condition normally indicated as “defective boundary condition”. We present and analyze several procedures by which this type of problems can be handled.K...

We consider the mixed formulation for Darcy’s flow in fractured media. We give a well-posedness result that does not rely on the imposition of pressure in part of the boundary of the fracture network, thus including a fully immersed fracture network. We present and analyze a mimetic finite difference formulation for the problem, providing convergen...

The aim of this work is to develop a computational model of the interplay between microcirculation and interstitial flow. Such phenomena are at the basis of the exchange of nutrients, wastes and pharmacological agents between the cardiovascular system and the organs. They are particularly interesting for the study of effective therapies to treat va...

This volume gathers contributions from participants of the Introductory School and the IHP thematic quarter on Numerical Methods for PDE, held in 2016 in Cargese (Corsica) and Paris, providing an opportunity to disseminate the latest results and envisage fresh challenges in traditional and new application fields. Numerical analysis applied to the a...

We consider an Extended Finite Elements method to handle the case of composite independent unstructured grids that lead to unfitted meshes. In particular, we address the case of two overlapped meshes, a background and a foreground one, where the thickness of the latter is smaller than the elements of the background mesh. This situation may lead to...

In this work, we consider the numerical approximation of the electromechanical coupling in the left ventricle with inclusion of the Purkinje network. The mathematical model couples the 3D elastodynamics and bidomain equations for the electrophysiology in the myocardium with the 1D monodomain equation in the Purkinje network. For the numerical solut...

This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the spatial domain. We propose a novel mass conservative multirate approach, that can be generalized to various im...

This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the spatial domain. We propose a novel mass conservative multirate approach, that can be generalized to various im...

A numerical procedure that combines an extended finite element formulation and a discontinuous Galerkin technique is presented, with the final aim of providing an effective tool for the simulation of three-dimensional (3D) fluid-structure interaction problems. In this work we consider a thick structure immersed in a fluid. We describe the numerical...

Numerical Analysis applied to the approximate resolution of Partial Differential Equations (PDEs) has become a key discipline in Applied Mathematics. One of the reasons for this success is that the wide availability of high-performance computational resources and the increase in the predictive capabilities of the models have significantly expanded...

We develop a novel Hybrid High-Order method for the simulation of Darcy flows in fractured porous media. The discretization hinges on a mixed formulation in the bulk region and on a primal formulation inside the fracture. Salient features of the method include a seamless treatment of nonconforming discretizations of the fracture, as well as the sup...

Mathematics and computer science has had enormous effects on industrial innovation, even instrumental to open up new type of business, like the Page Rank algorithm at the base of Google web search procedures. Industry 4.0 opens up new challenges to the industrial as well as to applied mathematicians. For instance, how to analyze the huge amount of,...

In this work, we consider the numerical approximation of the electrome-chanical coupling in the left ventricle with inclusion of the Purkinje network. The mathematical model couples the 3D elastodynamics and bido-main equations for the electrophysiology in the myocardium with the 1D monodomain equation in the Purkinje network. For the numerical sol...

LifeV is a library for the finite element (FE) solution of partial differential equations in one, two, and three dimensions. It is written in C++ and designed to run on diverse parallel architectures, including cloud and high performance computing facilities. In spite of its academic research nature, meaning a library for the development and testin...

We consider an Extended Finite Elements method to handle the case of composite independent grids that lead to unfitted meshes. We detail the corresponding discrete formulation for the Poisson problem with dis-continuous coefficients. We also provide some technical details for the 3D implementation. Finally, we provide some numerical examples with t...

We study the effects of transition to turbulence in abdominal aortic aneurysms (AAA). The presence of transitional effects in such districts is related to the heart pulsatility and the sudden change of diameter of the vessels, and has been recorded by means of clinical measures as well as of computational studies. Here we propose, for the first tim...

Abstract The present work proposes a novel method for the simulation of crack propagation in brittle elastic materials that combines two of the most popular approaches in literature. A large scale displacement solution is obtained with the well known extended finite elements method (XFEM), while propagation is governed by the solution of a local ph...

We present a computational modeling approach aimed at providing a preliminary description of the coupled effects of alternation of glaciation cycles, geochemical and mechanical compaction on the analysis of sedimentary basin formation spanning geological time scales. Our approach considers the complex interactions amongst Thermal-Hydrological-Mecha...

We develop a novel Hybrid High-Order method for the simulation of Darcy flows in fractured porous media. The discretization hinges on a mixed formulation in the bulk region and on a primal formulation inside the fracture. Salient features of the method include a seamless treatment of nonconforming discretizations of the fracture, as well as the sup...

We propose a mathematical model and a discretization strategy for the simulation of pressurized fractures in porous media accounting for the poroelastic effects due to the interaction of pressure and flow with rock deformations. The aim of the work is to develop a numerical scheme suitable to model the interplay among several fractures subject to f...

In this article we present some numerical techniques to increase efficiency and applicability of a flow-based upscaling procedure used to solve single and multi-phase flows in naturally fractured reservoirs. These geological formations may be characterized by hundreds up to hundreds of thousands of fractures, ranging from small to medium scales, sp...

We propose a mathematical model and a discretization strategy for the simulation of pressurized fractures in porous media accounting for the poroelastic effects due to the interaction of pressure and flow with rock deformations. The aim of the work is to develop a numerical scheme suitable to model the interplay among several fractures subject to f...

In this work we address the study of transition to turbulence effects in abdominal aortic aneurysms (AAA). The formation of transitional effects in such districts is caused by the heart pulsatility and the sudden change of diameter, and has been recorded by means of clinical measures and computational studies. Here we propose, for the first time, t...

An abridged version is now in https://doi.org/10.1051/m2an/2017028

A numerical procedure that combines an Extended Finite Element (XFEM) formulation and a Discontinuous Galerkin technique is presented, with the final aim of providing an effective tool for the simulation of three-dimensional fluid-structure interaction problems where the structure undergoes large displacements. In this work we consider thick struct...

Surface problems play a key role in several theoretical and applied fields. In this work the main focus is the presentation of a detailed analysis of the approximation of the classical porous media flow problem: the Darcy equation, where the domain is a regular surface. The formulation considers the mixed form and the numerical approximation adopts...

The book contains the abstract of all contributions to the SIMAI 2016 Congress held in Milano, Italy in September 2016.

Thanks to dimensional (or topological) model reduction techniques, small inclusions in a three-dimensional (3D) continuum can be described as one-dimensional (1D) concentrated sources, in order to reduce the computational cost of simulations. However, concentrated sources lead to singular solutions that still require computationally expensive grade...

Standard 3D mesh generation algorithms may produce a low quality tetrahedral mesh, i.e., a mesh where the tetrahedra have very small dihedral angles. In this paper, we propose a series of operations to recover these badly-shaped tetrahedra. In particular, we will focus on the shape of these undesired mesh elements by proposing a novel method to dis...

This volume collects selected contributions from the “Fourth Tetrahedron Workshop on Grid Generation for Numerical Computations”, which was held in Verbania, Italy in July 2013. The previous editions of this Workshop were hosted by the Weierstrass Institute in Berlin (2005), by INRIA Rocquencourt in Paris (2007), and by Swansea University (2010). T...

In this paper we deal with the numerical analysis of an upscaled model of a reactive flow in a porous medium, which describes the transport of solutes un- dergoing precipitation and dissolution, leading to the formation/degradation of crystals inside the porous matrix. The model is defined at the Darcy scale, and it is coupled to a Darcy flow chara...

This report collects the notes of two lectures given by L. Formaggia at the 7 th VKI Lecture Series on “Biological fluid dynamics” held at the Von Karman Institute, Belgium, on May 2003. They give a summary of some aspects of the research activity carried out by the authors at Politecnico di Milano and at EPFL, Lausanne, under the direction of Prof...

Stent modeling represents a challenging task from both the theoretical and numerical viewpoints, due to its multi-physics nature and to the complex geometrical configuration of these devices. In this light, dimensional model reduction enables a comprehensive geometrical and physical description of stenting at affordable computational costs. In this...

In finite element formulations, transport dominated problems are often stabilised through the Streamline-Upwind-Petrov–Galerkin (SUPG) method. Its application is straightforward when the problem at hand is solved using Galerkin methods. Applications of boundary integral formulations often resort to collocation techniques which are computationally m...

Slides of a webinar given in 2015. Video on https://youtu.be/38sUNd-ZgkQ

Segmentation of patient-specific vascular segments of interest from medical images is an important topic for numerous applications. Despite the great importance of having semi-automatic segmentation methods in this field, the process of image segmentation is still based on several operator-dependent steps which make large-scale segmentation a non t...