相关论文: Enriched Immersed Finite Element and Isogeometric …
The Finite Element Method (FEM) is a powerful computational tool for solving partial differential equations (PDEs). Although commercial and open-source FEM software packages are widely available, an independent implementation of FEM…
In this paper, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of…
This paper presents a technique for stress and fracture analysis by using the scaled boundary finite element method (SBFEM) with quadtree mesh of high-order elements. The cells of the quadtree mesh are modelled as scaled boundary polygons…
The increased availability of observation data from engineering systems in operation poses the question of how to incorporate this data into finite element models. To this end, we propose a novel statistical construction of the finite…
Topology optimization has emerged as a popular approach to refine a component's design and increase its performance. However, current state-of-the-art topology optimization frameworks are compute-intensive, mainly due to multiple finite…
Accurately, efficiently, and stably computing complex fluid flows and their evolution near solid boundaries over long horizons remains challenging. Conventional numerical solvers require fine grids and small time steps to resolve near-wall…
In the current practices of both industry and academia, the convergence and accuracy of finite element calculations are closely related to the methods and quality of mesh generation. For years, the research on high-quality mesh generation…
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…
Finite element methods typically require a high resolution to satisfactorily approximate micro and even macro patterns of an underlying physical model. This issue can be circumvented by appropriate multiscale strategies that are able to…
We consider the reliable implementation of high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems. We construct a reliable algorithm to merge small interface elements with their…
Since the seminal work of Idelsohn, O\~nate and Del-Pin (2004), the Particle Finite Element Method (PFEM) has relied on a Delaunay triangulation and the Alpha--Shape (AS) algorithm in the remeshing process. This approach guarantees a good…
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined with Shishkin meshes to obtain a stable parameter-uniform…
In this paper, we develop and analyze a trilinear immersed finite element method for solving three-dimensional elliptic interface problems. The proposed method can be utilized on interface-unfitted meshes such as Cartesian grids consisting…
To solve large-scale or high-resolution topology optimization problem, a novel algorithm is developed based on modified bi-directional evolutionary structure optimization (BESO) and extended finite element method (XFEM). Within XFEM, a set…
Neural operators aim to learn mappings between infinite-dimensional function spaces, but their performance often degrades on complex or irregular geometries due to the lack of geometry-aware representations. We propose the Finite Element…
In this paper, we propose a new approach -- the Tempered Finite Element Method (TFEM) -- that extends the Finite Element Method (FEM) to classes of meshes that include zero-measure or nearly degenerate elements for which standard FEM…
We present an efficient algorithmic framework for constructing multi-level hp-bases that uses a data-oriented approach that easily extends to any number of dimensions and provides a natural framework for performance-optimized…
Modeling of physical systems includes extensive use of software packages that implement the accurate finite element method for solving differential equations considered along with the appropriate initial and boundary conditions. When the…
We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called Phi-FEM, that uses the…
This work investigates finite element approximations for a general class of elliptic hemivariational inequalities arising in semipermeable media. The proposed model incorporates non-isotropic and heterogeneous diffusion coefficients,…