Related papers: A plastic correction algorithm for full-field elas…
An accurate, physically-based, and differentiable model of soft robots can unlock downstream applications in optimal control. The Finite Element Method (FEM) is an expressive approach for modeling highly deformable structures such as…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
The FE$^2$ homogenization algorithm for multiscale modeling iterates between the macroscale and the microscale (represented by a representative volume element) till convergence is achieved at every increment of macroscale loading. The…
Nonlocality brings many challenges to the implementation of finite element methods (FEM) for nonlocal problems, such as large number of queries and invoke operations on the meshes. Besides, the interactions are usually limited to Euclidean…
The quasicontinuum approximation is a method to reduce the atomistic degrees of freedom of a crystalline solid by piecewise linear interpolation from representative atoms that are nodes for a finite element triangulation. In regions of the…
The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…
The traditional element-based topology optimization based on material penalization typically aims at a 0/1 design. Our numerical experiments reveal that the compliance of a smooth design is overestimated when material properties of boundary…
We present a novel finite element analysis of inelastic structures containing Shape Memory Alloys (SMAs). Phenomenological constitutive models for SMAs lead to material nonlinearities, that require substantial computational effort to…
We investigate numerically a quasi-static elasticity system of Kachanov-type. To do so we propose an Euler time discretization combined with a suitable finite elements scheme (FEM) to handle the discretization is space. We use ODE-type…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
This paper outlines a rigorous variational-based multilevel Global-Local formulation for ductile fracture. Here, a phase-field formulation is used to resolve failure mechanisms by regularizing the sharp crack topology on the local state.…
We establish rigorous \emph{a posteriori} error bounds for a space-time finite element method of arbitrary order discretising linear wave problems in second order formulation. The method combines standard finite elements in space and…
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…
An efficient and reliable stress computation algorithm is presented, which is based on implicit integration of the local evolution equations of multiplicative finite-strain plasticity/viscoplasticity. The algorithm is illustrated by an…
This paper proposes an efficient algorithm for solving the Hartree--Fock equation combining a multilevel correction scheme with an adaptive refinement technique to improve computational efficiency. The algorithm integrates a multilevel…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…
A Finite Element procedure based on a full implicit backward Euler predictor/corrector scheme for the Cosserat continuum is here presented. Since this is based on invariants of the stress and couple stress tensors and on the spectral…
This paper presents the Virtual Element Method (VEM) for the modeling of crack propagation in 2D within the context of linear elastic fracture mechanics (LEFM). By exploiting the advantage of mesh flexibility in the VEM, we establish an…
Stochastic models of chemical systems are often analysed by solving the corresponding Fokker-Planck equation which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of…
In this paper we propose local approximation spaces for localized model order reduction procedures such as domain decomposition and multiscale methods. Those spaces are constructed from local solutions of the partial differential equation…