相关论文: Stabilization-free virtual element method for 2D t…

The Finite Element Method (FEM) is the gold standard for spatial discretization in numerical simulations for a wide spectrum of real-world engineering problems. Prototypical areas of interest include linear heat transfer and linear…

We present high-order, finite element-based Second Moment Methods (SMMs) for solving radiation transport problems in two spatial dimensions. We leverage the close connection between the Variable Eddington Factor (VEF) method and SMM to…

The finite element method (FEM) and the boundary element method (BEM) can numerically solve the Helmholtz system for acoustic wave propagation. When an object with heterogeneous wave speed or density is embedded in an unbounded exterior…

Rigorous computer simulations of propagating electromagnetic fields have become an important tool for optical metrology and design of nanostructured optical components. A vectorial finite element method (FEM) is a good choice for an…

This paper presents a matrix-free approach for implementing the shifted boundary method (SBM) in finite element analysis. The SBM is a versatile technique for solving partial differential equations on complex geometries by shifting boundary…

When the effects of relative motion at the solid object interfaces are not negligible, the contact method is required in the smoothed particle hydrodynamics (SPH) method to prevent virtual shear and tensile stresses. However, there is still…

We introduce a novel hybrid methodology combining classical finite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from finite element…

The numerical approximation of 2D elasticity problems is considered, in the framework of the small strain theory and in connection with the mixed Hellinger-Reissner variational formulation. A low-order Virtual Element Method (VEM) with…

The VEM approximation of eigenvalue problems usually involves the appropriate tuning of stabilization parameters, unless self-stabilizing or stabilization-free VEM are used. In this paper we prove that for elliptic self-adjoint eigenvalue…

The Virtual Element Method (VEM) is a novel family of numerical methods for approximating partial differential equations on very general polygonal or polyhedral computational grids. This work aims to propose a Balancing Domain Decomposition…

The objective of this article is to address the discretisation of fractured/faulted poromechanical models using 3D polyhedral meshes in order to cope with the geometrical complexity of faulted geological models. A polytopal scheme is…

The Virtual Element Method (VEM) is a new family of numerical methods for the approximation of partial differential equations, where the geometry of the polytopal mesh elements can be very general. The aim of this article is to extend the…

In this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave equation in a bidimensional setting. Curved elements are used to describe the domain boundary, as…

We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain which is a union of manifolds of different dimensions such that a $d$ dimensional component always resides on the boundary of a $d+1$…

A fluid-structure interaction technique for the simulation of inflatable structures is introduced. The presented finite-element/boundary-element (FEBE) technique couples an isogeometric finite element discretization of a flexible shell…

We present the design, convergence analysis and numerical investigations of the nonconforming virtual element method with Streamline Upwind/Petrov-Galerkin (VEM-SUPG) stabilization for the numerical resolution of…

We present a computational framework for simulating filaments interacting with rigid bodies through contact. Filaments are challenging to simulate due to their codimensionality, i.e., they are one-dimensional structures embedded in…

A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…

An important requirement in the standard finite element method (FEM) is that all elements in the underlying mesh must be tangle-free i.e., the Jacobian must be positive throughout each element. To relax this requirement, an isoparametric…

The hyperelastic materials would contribute to the intricacies of rough surface contact, primarily due to the heightened nonlinearity caused by stress concentration. In our previous research, an incremental contact model tailored for…