324 citations · 636 across the 33 of their papers we have counts for
34 papers
An embedding-aware continuum thin shell formulation
Abhishek Ghosh, Andrew McBride, Zhaowei Liu +3
Cutting-edge smart materials are transforming the domains of soft robotics, actuators, and sensors by harnessing diverse non-mechanical stimuli, such as electric and magnetic field…
Mixed-dimensional modeling of vascular tissues with reduced Lagrange multipliers
Camilla Belponer, Alfonso Caiazzo, Luca Heltai
This paper presents a numerical method for the simulation of multiscale materials composed of an elastic matrix and slender active inclusions. The setting is motivated by the model…
A fully-coupled nonlinear magnetoelastic thin shell formulation
Abhishek Ghosh, Andrew McBride, Zhaowei Liu +3
A geometrically exact dimensionally reduced order model for the nonlinear deformation of thin magnetoelastic shells is presented. The Kirchhoff-Love assumptions for the mechanical…
Exploiting high-contrast Stokes preconditioners to efficiently solve incompressible fluid-structure interaction problems
Michał Wichrowski, Piotr Krzyżanowski, Luca Heltai +1
In this work, we develop a new algorithm to solve large-scale incompressible time-dependent fluid--structure interaction (FSI) problems using a matrix-free finite element method in…
A comparison of non-matching techniques for the finite element approximation of interface problems
Daniele Boffi, Andrea Cangiani, Marco Feder +2
We perform a systematic comparison of various numerical schemes for the approximation of interface problems. We consider unfitted approaches in view of their application to possibl…
Reduced Lagrange multiplier approach for non-matching coupling of mixed-dimensional domains
Luca Heltai, Paolo Zunino
Many physical problems involving heterogeneous spatial scales, such as the flow through fractured porous media, the study of fiber-reinforced materials, or the modeling of the smal…
A Scharfetter-Gummerl stabilization scheme for HDG approximations of convection-diffusion problems
Stefano Piani, Luca Heltai, Wenyu Lei
We present a Scharfetter-Gummel (SG) stabilization scheme for high-order Hybrid Discontinuous Galerkin (HDG) approximations of convection-diffusion problems. The scheme is based on…
A weighted Hybridizable Discontinuous Galerkin method for drift-diffusion problems
Wenyu Lei, Stefano Piani, Patricio Farrell +2
In this work we propose a weighted hybridizable discontinuous Galerkin method (W-HDG) for drift-diffusion problems. By using specific exponential weights when computing the p…
Computational bifurcation analysis of hyperelastic thin shells
Zhaowei Liu, Andrew McBride, Abhishek Ghosh +5
The inflation of hyperelastic thin shells is an important and highly nonlinear problem that arises in multiple engineering applications involving severe kinematic and constitutive…
Data-driven solutions of ill-posed inverse problems arising from doping reconstruction in semiconductors
Stefano Piani, Patricio Farrell, Wenyu Lei +2
The non-destructive estimation of doping concentrations in semiconductor devices is of paramount importance for many applications ranging from crystal growth, the recent redefiniti…
Adaptive finite element approximations for elliptic problems using regularized forcing data
Luca Heltai, Wenyu Lei
We propose an adaptive finite element algorithm to approximate solutions of elliptic problems whose forcing data is locally defined and is approximated by regularization (or mollif…
Model hierarchies and higher-order discretisation of time-dependent thin-film free boundary problems with dynamic contact angle
Dirk Peschka, Luca Heltai
We present a mathematical and numerical framework for thin-film fluid flows over planar surfaces including dynamic contact angles. In particular, we provide algorithmic details and…
Vibration Analysis of Piezoelectric Kirchhoff-Love Shells based on Catmull-Clark Subdivision Surfaces
Zhaowei Liu, Andrew McBride, Prashant Saxena +3
An isogeometric Galerkin approach for analysing the free vibrations of piezoelectric shells is presented. The shell kinematics is specialised to infinitesimal deformations and foll…
Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems
Stefano Giani, Luka Grubišić, Luca Heltai +1
We present a perturbed subspace iteration algorithm to approximate the lowermost eigenvalue cluster of an elliptic eigenvalue problem. As a prototype, we consider the Laplace eigen…
A numerical study of the jerky crack growth in elastoplastic materials with localized plasticity
Gianni Dal Maso, Luca Heltai
We present a numerical implementation of a model of quasi-static crack growth in linearly elastic-perfectly plastic materials. We assume that the displacement is antiplane, and tha…
A priori error estimates of regularized elliptic problems
Luca Heltai, Wenyu Lei
Approximations of the Dirac delta distribution are commonly used to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution. In this w…
The deal.II finite element library: design, features, and insights
Daniel Arndt, Wolfgang Bangerth, Denis Davydov +7
deal.II is a state-of-the-art finite element library focused on generality, dimension-independent programming, parallelism, and extensibility. Herein, we outline its primary design…
Propagating geometry information to finite element computations
Luca Heltai, Wolfgang Bangerth, Martin Kronbichler +1
The traditional workflow in continuum mechanics simulations is that a geometry description -- for example obtained using Constructive Solid Geometry or Computer Aided Design tools…
Multiscale modeling of vascularized tissues via non-matching immersed methods
Luca Heltai, Alfonso Caiazzo
We consider a multiscale approach based on immersed methods for the efficient computational modeling of tissues composed of an elastic matrix (in two or three-dimensions) and a thi…
Multiscale modeling of fiber reinforced materials via non-matching immersed methods
Giovanni Alzetta, Luca Heltai
Fiber reinforced materials (FRMs) can be modeled as bi-phasic materials, where different constitutive behaviors are associated with different phases. The numerical study of FRMs th…
Error estimates in weighted Sobolev norms for finite element immersed interface methods
Luca Heltai, Nella Rotundo
When solving elliptic partial differential equations in a region containing immersed interfaces (possibly evolving in time), it is often desirable to approximate the problem using…
Quasi-optimal mesh sequence construction through Smoothed Adaptive Finite Element Method
Ornela Mulita, Stefano Giani, Luca Heltai
We propose a new algorithm for Adaptive Finite Element Methods (AFEMs) based on smoothing iterations (S-AFEM), for linear, second-order, elliptic partial differential equations (PD…
Accelerating the iterative solution of convection-diffusion problems using singular value decomposition
Giuseppe Pitton, Luca Heltai
The discretization of convection-diffusion equations by implicit or semi-implicit methods leads to a sequence of linear systems usually solved by iterative linear solvers such as G…
NURBS-SEM: a hybrid spectral element method on NURBS maps for the solution of elliptic PDEs on surfaces
Giuseppe Pitton, Luca Heltai
Non Uniform Rational B-spline (NURBS) patches are a standard way to describe complex geometries in Computer Aided Design tools, and have gained a lot of popularity in recent years…