相关论文: Three dimensional seepage analysis using a polyhed…
A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…
We investigate the isogeometric analysis for surface PDEs based on the extended Loop subdivision approach. The basis functions consisting of quartic box-splines corresponding to each subdivided control mesh are utilized to represent the…
One remarkable feature of virtual element methods (VEMs) is their great flexibility and robustness when used on almost arbitrary polytopal meshes. This very feature makes it widely used in both fitted and unfitted mesh methods. Despite…
The statistical finite element method (StatFEM) is an emerging probabilistic method that allows observations of a physical system to be synthesised with the numerical solution of a PDE intended to describe it in a coherent statistical…
The eXtended Finite Element Method (XFEM) is used to solve interface problems with an unfitted mesh. We present an implementation of the XFEM in the FEM-library deal.II. The main parts of the implementation are (i) the appropriate…
The formulation of a new prism finite element is presented for the nonlinear analysis of solid shells subject to large strains and large displacements. The element is based on hierarchical, heterogeneous, and anisotropic shape functions. As…
In this work we propose a simple but effective high order polynomial correction allowing to enhance the consistency of all kind of boundary conditions for the Euler equations (Dirichlet, characteristic far-field and slip-wall), both in 2D…
We extend the shifted boundary method (SBM) to the simulation of incompressible fluid flow using immersed octree meshes. Previous work on SBM for fluid flow primarily utilized two- or three-dimensional unstructured tetrahedral grids.…
This paper presents a new methodology for structural reliability analysis via stochastic finite element method (SFEM). A novel sample-based SFEM is firstly used to compute structural stochastic responses of all spatial points at the same…
The boundary element method (BEM) provides an efficient numerical framework for solving multiple scattering problems in unbounded homogeneous domains, since it reduces the discretization to the domain boundaries, thereby condensing the…
We develop an efficient and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the regularization technique of Chen, Holst, and Xu; this technique made possible the first a…
The peridynamic theory brings advantages in dealing with discontinuities, dynamic loading, and non-locality. The integro-differential formulation of peridynamics poses challenges to numerical solutions of complicated and practical problems.…
Deformable elastic bodies in viscous and viscoelastic media constitute a large portion of synthetic and biological complex fluids. We present a parallelized 3D-simulation methodology which fully resolves the momentum balance in the solid…
This paper considers the reconstruction of a defect in a two-dimensional waveguide during non-destructive ultrasonic inspection using a derivative-based optimization approach. The propagation of the mechanical waves is simulated by the…
In this paper, we construct a combined multiscale finite element method (MsFEM) using the Local Orthogonal Decomposition (LOD) technique to solve the multiscale problems which may have singularities in some special portions of the…
The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present $\textbf{Qu-FEM}$, a fault-tolerant era quantum algorithm for the finite element method. In contrast to…
Optimally convergent (with respect to the regularity) quadratic finite element method for two dimensional obstacle problem on simplicial meshes is studied in (Brezzi, Hager, Raviart, Numer. Math, 28:431--443, 1977). There was no analogue of…
Polytopal Element Methods (PEM) allow to solve differential equations on general polygonal and polyhedral grids, potentially offering great flexibility to mesh generation algorithms. Differently from classical finite element methods, where…
Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the domain limits the accuracy of finite element methods based on…
The recently proposed soft finite element method (SoftFEM) reduces the stiffness (condition numbers), consequently improving the overall approximation accuracy. The method subtracts a least-square term that penalizes the gradient jumps…