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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…
Modeling arbitrarily large deformations of surfaces smoothly embedded in three-dimensional space is challenging. The difficulties come from two aspects: the existing geometry processing or forward simulation methods penalize the difference…
Algorithms that promise to leverage resources of quantum computers efficiently to accelerate the finite element method have emerged. However, the finite element method is usually incorporated into a high-level numerical scheme which allows…
This work presents a novel physics-informed deep learning based super-resolution framework to reconstruct high-resolution deformation fields from low-resolution counterparts, obtained from coarse mesh simulations or experiments. We leverage…
In this paper we present a methodology for increasing the accuracy and accelerating the convergence of numerical methods for solution of Maxwell's equations in the frequency domain by taking into account the be-havior of the electromagnetic…
Recovery type a posteriori error estimators are popular, particularly in the engineering community, for their computationally inexpensive, easy to implement, and generally asymptotically exactness. Unlike the residual type error estimators,…
Nowadays, several models of unidimensional fluid jets exploit discrete element methods. In some cases, as for models aiming at describing the electrospinning nanofabrication process of polymer fibers, discrete element methods suffer a non…
The Poisson-Boltzmann equation is a widely used model to study the electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
In the present thesis, a computational framework for the analysis of the deformation and damage phenomena occurring at the micro-scale of polycrystalline materials is presented. Micro-mechanics studies are commonly performed using the…
In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…
This paper establishes a universal framework for the nonlocal modeling of anisotropic damage at finite strains. By the combination of two recent works, the new framework allows for the flexible incorporation of different established…
In this work, we extend the recently proposed adaptive phase field method to model fracture in orthotropic functionally graded materials (FGMs). A recovery type error indicator combined with quadtree decomposition is employed for adaptive…
The phase field fracture method has emerged as a promising computational tool for modelling a variety of problems including, since recently, hydrogen embrittlement and stress corrosion cracking. In this work, we demonstrate the potential of…
This work outlines a diffuse interface method for the study of fracture and fragmentation in ductile metals at high strain-rates in Eulerian finite volume simulations. The work is based on an existing diffuse interface method capable of…
Variational phase-field models of fracture are widely used to simulate nucleation and propagation of cracks in brittle materials. They are based on the approximation of the solutions of free-discontinuity fracture energy by two smooth…
This paper presents the first time implementation of the eXtended Finite Element Method (XFEM) in the general purpose commercial software COMSOL Multiphysics. An enrichment strategy is proposed, consistent with the structure of the…
In the past few years, following the differentiable programming paradigm, there has been a growing interest in computing the gradient information of physical processes (e.g., physical simulation, image rendering). However, such processes…
We propose a mathematical model that combines elastic, viscous and porous effects with growth or shrinkage due to microstructural changes. This phenomenon is important in tissue or tumor growth, as well as in dermal contraction. Although…
Numerical and analytical methods are developed for the investigation of contact sets in electrostatic-elastic deflections modeling micro-electro mechanical systems. The model for the membrane deflection is a fourth-order semi-linear partial…