Related papers: Direct coupling of continuum and shell elements in…
Many tasks in geometry processing are modeled as variational problems solved numerically using the finite element method. For solid shapes, this requires a volumetric discretization, such as a boundary conforming tetrahedral mesh.…
Simulating the deformation of fractured media requires the coupling of different models for the deformation of fractures and the formation surrounding them. We consider a cell-centered finite-volume approach, termed the multipoint stress…
We show convergence of a cell-centered finite volume discretization for linear elasticity. The discretization, termed the MPSA method, was recently proposed in the context of geological applications, where cell-centered variables are often…
The topologies of existing interface elements used to discretize cohesive cracks are such that they can be used to compute the relative displacements (displacement discontinuities) of two opposing segments (in 2D) or of two opposing facets…
The multi-scale nature of architectured materials raises the need for advanced experimental methods suitable for the identification of their effective properties, especially when their size is finite and they undergo extreme deformations.…
In this paper we develop a simple finite element method for simulation of embedded layers of high permeability in a matrix of lower permeability using a basic model of Darcy flow in embedded cracks. The cracks are allowed to cut through the…
This paper presents a general, nonlinear isogeometric finite element formulation for rotation-free shells with embedded fibers that captures anisotropy in stretching, shearing, twisting and bending -- both in-plane and out-of-plane. These…
We consider variational problems that model the bending behavior of curves that are constrained to belong to given hypersurfaces. Finite element discretizations of corresponding functionals are justified rigorously via Gamma-convergence.…
Many problems in electrical engineering or fluid mechanics can be modeled by parabolic-elliptic interface problems, where the domain for the exterior elliptic problem might be unbounded. A possibility to solve this class of problems…
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…
Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…
We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are…
Soft robots achieve functionality through tight coupling among geometry, material composition, and actuation. As a result, effective design optimization requires these three aspects to be considered jointly rather than in isolation. This…
In this manuscript, we extend the variational multiscale enrichment (VME) method to model the dynamic response of hyperelastic materials undergoing large deformations. This approach enables the simulation of wave propagation under…
Self-assembly in natural and synthetic molecular systems can create complex aggregates or materials whose properties and functionality rises from their internal structure and molecular arrangement. The key microscopic features that control…
In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…
Fundamental theories and models of many-body physics can be probed in experiments on ultracold atoms held in place by electromagnetic fields. In particular, of considerable interest are systems under curved confinement, since they can yield…
Interpolation methods for nonlinear finite element discretizations are commonly used to eliminate the computational costs associated with the repeated assembly of the nonlinear systems. While the group finite element formulation…
In this contribution, a finite element scheme to impose mixed boundary conditions without introducing Lagrange multipliers is presented for hyperbolic systems described as port-Hamiltonian systems. The strategy relies on finite element…
Flow in fractured porous media represents a challenge for discretization methods due to the disparate scales and complex geometry. Herein we propose a new discretization, based on the mixed finite element method and mortar methods. Our…