Jad Dabaghi

@article{dabaghi_3076,

title = {Structure-preserving reduced order model for parametric cross-diffusion systems},

author = {Jad Dabaghi and Virginie Ehrlacher},

url = {https://doi.org/10.1051/m2an/2024026},

year  = {2024},

date = {2024-06-01},

journal = {Esaim-Mathematical Modelling And Numerical Analysis-Modelisation Mathematique Et Analyse Numerique},

volume = {58},

number = {3},

pages = {1201-1227},

abstract = {In this work, we construct a structure-preserving Galerkin reduced-order model for the

resolution of parametric cross-diffusion systems. Cross-diffusion systems are often used to model the

evolution of the concentrations or volumic fractions of mixtures composed of different species, and can

also be used in population dynamics (as for instance in the SKT system). These systems often read

as nonlinear degenerated parabolic partial differential equations, the numerical resolutions of which

are highly expensive from a computational point of view. We are interested here in cross-diffusion

systems which exhibit a so-called entropic structure, in the sense that they can be formally written as

gradient flows of a certain entropy functional which is actually a Lyapunov functional of the system.

In this work, we propose a new reduced-order modelling method, based on a reduced basis paradigm,

for the resolution of parameter-dependent cross-diffusion systems. Our method preserves, at the level

of the reduced-order model, the main mathematical properties of the continuous solution, namely

mass conservation, non-negativeness, preservation of the volume-filling property and entropy-entropy

dissipation relationship. The theoretical advantages of our approach are illustrated by several numerical

experiments.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{dabaghi_2758,

title = {Computation of the self-diffusion coefficient with low-rank tensor methods: application to the simulation of a cross-diffusion system},

author = {Jad Dabaghi and Virginie Ehrlacher and Christoph Strossner},

url = {https://www.esaim-proc.org/articles/proc/abs/2023/02/proc2307309/proc2307309.html},

year  = {2023},

date = {2023-09-01},

journal = {Esaim: proceedings and surveys},

volume = {73},

pages = {173-186},

abstract = {Cross-diffusion systems arise as hydrodynamic limits of lattice multi-species interacting particle models. The objective of this work is to provide a numerical scheme for the simulation of the cross-diffusion system identified in [J. Quastel, Comm. Pure Appl. Math., 45 (1992), pp. 623-679]. To simulate this system, it is necessary to provide an approximation of the so-called self-diffusion coefficient matrix of the tagged particle process. Classical algorithms for the computation of this matrix are based on the estimation of the long-time limit of the average mean square displacement of the particle. In this work, as an alternative, we propose a novel approach for computing the self-diffusion coefficient using deterministic low-rank approximation techniques, as the minimum of a high-dimensional optimization problem. The computed self-diffusion coefficient is then used for the simulation of the cross-diffusion system using an implicit finite volume scheme.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{dabaghi_2223,

title = {Tensor approximation of the self-diffusion matrix of tagged particle processes},

author = {Jad Dabaghi and Virginie Ehrlacher and Christoph Strossner},

url = {https://www.sciencedirect.com/science/article/pii/S0021999123001122},

year  = {2023},

date = {2023-05-01},

journal = {Journal Of Computational Physics},

volume = {480},

pages = {112017},

abstract = {The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of empirical means of deviations of some stochastic processes, and are thus subject to statistical noise, we propose here a tensor method in order to compute an approximation of the solution of a high-dimensional quadratic optimization problem, which enables to obtain a numerical approximation of the self-diffusion matrix. The tensor method we use here relies on an iterative scheme which builds low-rank approximations of the quantity of interest and on a carefully tuned variance reduction method so as to evaluate the various terms arising in the functional to minimize. In particular, we numerically observe here that it is much less subject to statistical noise than classical approaches.},

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pubstate = {published},

tppubtype = {article}

}

@article{zoia_1969,

title = {A hybrid parareal Monte-Carlo algorithm for parabolic problems},

author = {Andrea Zoia and Yvon Maday and Jad Dabaghi},

url = {https://www.sciencedirect.com/science/article/abs/pii/S0377042722004071},

year  = {2023},

date = {2023-03-01},

journal = {Journal Of Computational And Applied Mathematics},

volume = {420},

pages = {114800},

abstract = {In this work, we propose a hybrid Monte Carlo/deterministic ??parareal-in-time'' approach devoted to accelerating Monte Carlo simulations over massively parallel computing environments for the simulation of time-dependent problems.

This parareal approach iterates on two different solvers: a low-cost ??coarse'' solver

based on a very cheap deterministic Galerkin scheme and a ??fine'' solver based on a

high-fidelity Monte Carlo resolution.

In a set of benchmark numerical experiments based on a toy model concerning

the time-dependent diffusion equation, we compare our hybrid parareal strategy with

a standard full Monte Carlo solution. In particular, we show that for a large number

of processors, our hybrid strategy significantly reduces the computational time of the

simulation while preserving its accuracy. The convergence properties of the proposed

Monte Carlo/deterministic parareal strategy are also discussed.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{dabaghi_1969,

title = {A hybrid parareal Monte-Carlo algorithm for parabolic problems},

author = {Jad Dabaghi and Yvon Maday and Andrea Zoia},

url = {https://www.sciencedirect.com/science/article/abs/pii/S0377042722004071},

year  = {2023},

date = {2023-03-01},

journal = {Journal Of Computational And Applied Mathematics},

volume = {420},

pages = {114800},

abstract = {In this work, we propose a hybrid Monte Carlo/deterministic ??parareal-in-time'' approach devoted to accelerating Monte Carlo simulations over massively parallel computing environments for the simulation of time-dependent problems.

This parareal approach iterates on two different solvers: a low-cost ??coarse'' solver

based on a very cheap deterministic Galerkin scheme and a ??fine'' solver based on a

high-fidelity Monte Carlo resolution.

In a set of benchmark numerical experiments based on a toy model concerning

the time-dependent diffusion equation, we compare our hybrid parareal strategy with

a standard full Monte Carlo solution. In particular, we show that for a large number

of processors, our hybrid strategy significantly reduces the computational time of the

simulation while preserving its accuracy. The convergence properties of the proposed

Monte Carlo/deterministic parareal strategy are also discussed.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{dabaghi_2730,

title = {A unified framework for high-order numerical discretizations of variational inequalities},

author = {Jad Dabaghi and Guillaume Delay},

url = {https://www.sciencedirect.com/science/article/pii/S0898122121000857},

year  = {2021},

date = {2021-06-01},

journal = {Computers & Mathematics With Applications},

volume = {92},

pages = {62-75},

abstract = {We present in this work a unified framework for elliptic variational inequalities that gathers several problems in contact mechanics like the unilateral contact of one or two membranes or the Signorini problem. We study a family of Galerkin numerical schemes that discretize this framework. We prove the well-posedness of the discrete problem and we show that it is equivalent to a saddle-point mixed formulation containing complementarity constraints. To solve the arising nonlinear problem, we employ a semismooth Newton method and we prove local convergence properties. The abstract framework is then applied to the discretization of the unilateral contact between two membranes. We propose to discretize this problem with a finite element (FEM), a discontinuous Galerkin (dG), and a hybrid high-order (HHO) methods. We also adapt the semismooth Newton algorithm, including a static condensation procedure for the HHO method. Finally, we run numerical experiments for the FEM and HHO discretizations and compare their behavior.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{dabaghi_2732,

title = {A posteriori estimates distinguishing the error components and adaptive stopping criteria for numerical approximations of parabolic variational inequalities},

author = {Jad Dabaghi and Vincent Martin and Martin Vohralik},

url = {https://www.sciencedirect.com/science/article/pii/S0045782520302899},

year  = {2020},

date = {2020-08-01},

journal = {Computer Methods In Applied Mechanics And Engineering},

volume = {367},

pages = {113105},

abstract = {We consider in this paper a model parabolic variational inequality. This problem is discretized with conforming Lagrange finite elements of order p?1 in space and with the backward Euler scheme in time. The nonlinearity coming from the complementarity constraints is treated with any semismooth Newton algorithm and we take into account in our analysis an arbitrary iterative algebraic solver. In the case p=1, when the system of nonlinear algebraic equations is solved exactly, we derive an a posteriori error estimate on both the energy error norm and a norm approximating the time derivative error. When p?1, we provide a fully computable and guaranteed a posteriori estimate in the energy error norm which is valid at each step of the linearization and algebraic solvers. Our estimate, based on equilibrated flux reconstructions, also distinguishes the discretization, linearization, and algebraic error components. We build an adaptive inexact semismooth Newton algorithm based on stopping the iterations of both solvers when the estimators of the corresponding error components do not affect significantly the overall estimate. Numerical experiments are performed with the semismooth Newton-min algorithm and the semismooth Newton-Fischer-Burmeister algorithm in combination with the GMRES iterative algebraic solver to illustrate the strengths of our approach.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{dabaghi_2605,

title = {Adaptive inexact semismooth Newton methods for the contact problem between two membranes},

author = {Jad Dabaghi and Vincent Martin and Martin Vohralik},

url = {https://link.springer.com/article/10.1007/s10915-020-01264-3},

year  = {2020},

date = {2020-07-01},

journal = {Journal Of Scientific Computing},

volume = {84},

number = {28},

pages = {-},

abstract = {We propose an adaptive inexact version of a class of semismooth Newton methods that is aware of the continuous (variational) level. As a model problem, we study the system of variational inequalities describing the contact between two membranes. This problem is discretized with conforming finite elements of order , yielding a nonlinear algebraic system with inequalities. We consider any iterative semismooth linearization algorithm like the Newton-min or the Newton-Fischer-Burmeister which we complement by any iterative linear algebraic solver. We then derive an a posteriori estimate on the error between the exact solution at the continuous level and the approximate solution which is valid at any step of the linearization and algebraic resolutions. Our estimate is based on flux reconstructions in discrete subspaces of and on potential reconstructions in discrete subspaces of satisfying the constraints. It distinguishes the discretization, linearization, and algebraic components of the error. Consequently, we can formulate adaptive stopping criteria for both solvers, giving rise to an adaptive version of the considered inexact semismooth Newton algorithm. Under these criteria, the efficiency of the leading estimates is also established, meaning that we prove them equivalent with the error up to a generic constant. Numerical experiments for the Newton-min algorithm in combination with the GMRES algebraic solver confirm the efficiency of the developed adaptive method.},

keywords = {},

pubstate = {published},

tppubtype = {article}

}

@article{ben_gharbia_2733,

title = {A posteriori error estimates for a compositional two-phase flow with nonlinear complementarity constraints},

author = {Ibtihel Ben Gharbia and Jad Dabaghi and Vincent Martin and Martin Vohralik},

url = {https://link.springer.com/article/10.1007/s10596-019-09909-5#citeas},

year  = {2020},

date = {2020-06-01},

journal = {Computational Geosciences},

volume = {24},

pages = {1031-1055},

abstract = {In this work, we develop an a posteriori-steered algorithm for a compositional two-phase flow with exchange of components between the phases in porous media. As a model problem, we choose the two-phase liquid-gas flow with appearance and disappearance of the gas phase formulated as a system of nonlinear evolutive partial differential equations with nonlinear complementarity constraints. The discretization of our model is based on the backward Euler scheme in time and the finite volume scheme in space. The resulting nonlinear system is solved via an inexact semismooth Newton method. The key ingredients for the a posteriori analysis are the discretization, linearization, and algebraic flux reconstructions allowing to devise estimators for each error component. These enable to formulate criteria for stopping the iterative algebraic solver and the iterative linearization solver whenever the corresponding error components do not affect significantly the overall error. Numerical experiments are performed using the Newton-min algorithm as well as the Newton-Fischer-Burmeister algorithm in combination with the GMRES iterative linear solver to show the efficiency of the proposed adaptive method.},

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pubstate = {published},

tppubtype = {article}

}