Daniele Prada

Daniele Prada
IMATI-CNR Pavia

PhD

About

34
Publications
11,329
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243
Citations
Additional affiliations
January 2013 - present
Indiana University-Purdue University Indianapolis
Position
  • PhD Student

Publications

Publications (34)
Preprint
We analyze and validate the virtual element method combined with a projection approach similar to the one in [1, 2], to solve problems on two dimensional domains with curved boundaries approximated by polygonal domains obtained as the union of squared elements out of a uniform structured mesh, such as the one that naturally arise when the domain is...
Article
We consider a multiscale problem modeling the flow of a fluid through a deformable porous medium, described by a system of partial differential equations (PDEs), connected with a lumped hydraulic circuit, described by a system of ordinary differential equations (ODEs). This PDE/ODE coupled problem includes interface conditions enforcing the continu...
Preprint
Full-text available
We analyze the local accuracy of the virtual element method. More precisely, we prove an error bound similar to the one holding for the finite element method, namely, that the local $H^1$ error in a interior subdomain is bounded by a term behaving like the best approximation allowed by the local smoothness of the solution in a larger interior subdo...
Preprint
Full-text available
In the framework of virtual element discretizazions, we address the problem of imposing non homogeneous Dirichlet boundary conditions in a weak form, both on polygonal/polyhedral domains and on two/three dimensional domains with curved boundaries. We consider a Nitsche's type method [43,41], and the stabilized formulation of the Lagrange multiplier...
Article
Polytopal Element Methods (PEM) allow us solving differential equations on general polygonal and polyhedral grids, potentially offering great flexibility to mesh generation algorithms. Differently from classical finite element methods, where the relation between the geometric properties of the mesh and the performances of the solver are well known,...
Article
In this paper, we introduce a new stabilization for discontinuous Galerkin methods for the Poisson problem on polygonal meshes, which induces optimal convergence rates in the polynomial approximation degree [Formula: see text]. The stabilization is obtained by penalizing, in each mesh element [Formula: see text], a residual in the norm of the dual...
Article
We address the issue of designing robust stabilization terms for the nonconforming virtual element method. To this end, we transfer the problem of defining the stabilizing bilinear form from the elemental nonconforming virtual element space, whose functions are not known in closed form, to the dual space spanned by the known functionals providing t...
Preprint
Full-text available
We address the issue of designing robust stabilization terms for the nonconforming virtual element method. To this end, we transfer the problem of defining the stabilizing bilinear form from the elemental nonconforming virtual element space, whose functions are not known in closed form, to the dual space spanned by the known functionals providing t...
Preprint
Full-text available
In this work we report some results, obtained within the framework of the ERC Project CHANGE, on the impact on the performance of the virtual element method of the shape of the polygonal elements of the underlying mesh. More in detail, after reviewing the state of the art, we present a) an experimental analysis of the convergence of the VEM under c...
Preprint
Full-text available
We introduce a new stabilization for discontinuous Galerkin methods for the Poisson problem on polygonal meshes, which induces optimal convergence rates in the polynomial approximation degree $p$. In the setting of [S. Bertoluzza and D. Prada, A polygonal discontinuous Galerkin method with minus one stabilization, ESAIM Math. Mod. Numer. Anal. (DOI...
Article
We propose a Discontinuous Galerkin method for the Poisson equation on polygonal tessellations in two dimensions, stabilized by penalizing, locally in each element K, a residual term involving the fluxes, measured in the norm of the dual of H 1 (K). The scalar product corresponding to such a norm is numerically realized via the introduction of a (m...
Article
Full-text available
We deal with the finite element tearing and interconnecting dual primal preconditioner for elliptic problems discretized by the virtual element method. We extend the result of [S. Bertoluzza, M. Pennacchio, and D. Prada, Calcolo, 54 (2017), pp. 1565-1593] to the three dimensional case. We prove polylogarithmic condition number bounds, independent o...
Preprint
Full-text available
In this paper we consider the Virtual Element discretization of a minimal surface problem, a quasi-linear elliptic partial differential equation modeling the problem of minimizing the area of a surface subject to a prescribed boundary condition. We derive optimal error estimate and present several numerical tests assessing the validity of the theor...
Chapter
This chapter provides an overview of the main structural and functional properties of the ocular vasculature. Four major circulatory systems within the eye are considered, namely those nourishing the retina, the optic nerve head, the choroid, and the anterior segment. Some aspects related to vascular regulation and innervation are also discussed, a...
Chapter
This chapter examines the assessment of ocular hemodynamics in health and disease. Beginning with a discussion on ocular perfusion pressure and the physical principles, we systematically present the conceptual basis and details of blood flow measurement technology, paying particular attention to the scientific and clinical strengths and weaknesses...
Chapter
This chapter reviews the abundant evidence of correlations between vascular alterations and ocular diseases. In particular, we discuss retinal diseases, including age-related macular degeneration, diabetic retinopathy and retinal vessel occlusions, glaucoma, and non-arteritic ischemic optic neuropathy. Current inconsistencies among studies and outs...
Article
Full-text available
We deal with the virtual element method (VEM) for solving the Poisson equation on a domain Ω with curved boundary. Given a polygonal approximation Ω_h of the domain Ω, the standard order m VEM [6], for m increasing, leads to a suboptimal convergence rate. We adapt the approach of [14] to VEM and we prove that an optimal convergence rate can be achi...
Preprint
Full-text available
Polytopal Element Methods (PEM) allow to solve differential equations on general polygonal and polyhedral grids, potentially offering great flexibility to mesh generation algorithms. Differently from classical finite element methods, where the relation between the geometric properties of the mesh and the performances of the solver are well known, t...
Chapter
Advancements in imaging technologies over the past several decades have allowed for the identification of non-intraocular pressure (IOP) processes involved in glaucomatous optic neuropathy. Perhaps the most commonly cited non-IOP risk factors are impaired ocular circulation and/or faulty vascular regulation and vasospasm [1, 2]. Other important con...
Chapter
Full-text available
We analyze the performance of a state-of-the-art domain decomposition approach, the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) method (Toselli and Widlund, Domain decomposition methods—algorithms and theory. Springer series in computational mathematics, vol 34, 2005), for the efficient solution of very large linear systems ari...
Preprint
Full-text available
We investigate the performance of algebraic multigrid methods for the solution of the linear system of equations arising from a Virtual Element discretization. We provide numerical experiments on very general polygonal meshes for a model elliptic problem with and without highly heterogeneous diffusion coefficients and we draw conclusions regarding...
Preprint
We deal with the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) preconditioner for elliptic problems discretized by the virtual element method (VEM). We extend the result of [16] to the three dimensional case. We prove polylogarithmic condition number bounds, independent of the number of subdomains, the mesh size, and jumps in the...
Preprint
We deal with the virtual element method (VEM) for solving the Poisson equation on a domain $\Omega$ with curved boundaries. Given a polygonal approximation $\Omega_h$ of the domain $\Omega$, the standard order $m$ VEM [6], for $m$ increasing, leads to a suboptimal convergence rate. We adapt the approach of [14] to VEM and we prove that an optimal c...
Preprint
Full-text available
We deal with the virtual element method (VEM) for solving the Poisson equation on a domain $\Omega$ with curved boundaries. Given a polygonal approximation $\Omega_h$ of the domain $\Omega$, the standard order $m$ VEM [6], for $m$ increasing, leads to a suboptimal convergence rate. We adapt the approach of [14] to VEM and we prove that an optimal c...
Preprint
Full-text available
We propose an Hybridized Discontinuous Galerkin method on polygonal tessellation, with a stabilization term penalizing locally in each element $K$ a residual term involving the fluxes in the norm of the dual of $H^1(K)$. The scalar product corresponding to such a norm is numerically realized via the introduction of a (minimal) auxiliary space of VE...
Preprint
Full-text available
We analyze the performance of a state-of-the-art domain decomposition approach, the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) method, for the efficient solution of very large linear systems arising from elliptic problems discretized by the Virtual Element Method. We provide numerical experiments on a model linear elliptic pro...
Article
Full-text available
We build and analyze Balancing Domain Decomposition by Constraint (BDDC) and Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) preconditioners for elliptic problems discretized by the virtual element method (VEM). We prove polylogarithmic condition number bounds, independent of the number of subdomains, the mesh size, and jumps in th...
Article
We derive and analyze a hybridizable discontinuous Galerkin (HDG) method for approximating weak solutions to the equations of time-harmonic linear elasticity on a bounded Lipschitz domain in three dimensions. The real symmetry of the stress tensor is strongly enforced and its coefficients as well as those of the displacement vector field are approx...
Thesis
Full-text available
The interplay between biomechanics and blood perfusion in the optic nerve head (ONH) has a critical role in ocular pathologies, especially glaucomatous optic neuropathy. Elucidating the complex interactions of ONH perfusion and tissue structure in health and disease using current imaging methodologies is difficult, and mathematical modeling provide...
Article
Impairments of autoregulation and neurovascular coupling in the optic nerve head play a critical role in ocular pathologies, especially glaucomatous optic neuropathy. We critically review the literature in the field, integrating results obtained in clinical, experimental, and theoretical studies. We address the mechanisms of autoregulation and neur...
Article
Full-text available
In this paper, a general, robust, and automatic parameter extraction of nonlinear compact models is presented. The parameter extraction is based on multiobjective optimization using evolutionary algorithms which allow fitting of several highly nonlinear and highly conflicting characteristics simultaneously. Two multiobjective evolutionary algorithm...
Article
In this work we present a mathematical model for the coupling between biomechanics and hemodynamics in the lamina cribrosa, a thin porous tissue at the base of the optic nerve head which is thought to be the site of injury in ocular neurodegenerative diseases such as glaucoma. In this exploratory two-dimensional investigation, the lamina cribrosa i...
Conference Paper
Full-text available
The “lumped charge” power diode compact model is extended including impact ionization while maintaining the low computational cost. The new model can better reproduce the shape of the current peak during reverse recovery, allowing for more predictive EMI/EMC simulations. The parameter extraction procedure is also improved and automated through mult...

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