Related papers: A Finite Element Computational Framework for Activ…
Phase transition problems on curved surfaces can lead to a panopticon of fascinating patterns. In this paper we consider finite element approximations of phase field models with a spatially inhomogeneous and anisotropic surface energy…
Chaotic free surface flows are challenging problems to simulate numerically, mainly due to the significant changes in geometry and frequent topological changes. Methods that track the evolution of the fluid in a Lagrangian formulation are a…
Differential equations on metric graphs can describe many phenomena in the physical world but also the spread of information on social media. To efficiently compute the solution is a hard task in numerical analysis. Solving a design…
In affine formation control problems, the construction of the framework with universal rigidity and affine localizability is a critical prerequisite, but it has not yet been well addressed, especially when additional agents join the…
Edge features contain important information about graphs. However, current state-of-the-art neural network models designed for graph learning, e.g. graph convolutional networks (GCN) and graph attention networks (GAT), adequately utilize…
We propose a hybrid method, the Neural Enrichment Finite Element Method (NEFEM), designed for problems involving strong oscillations or interface problems with weak discontinuities. This method is based on the stable generalized finite…
Achieving accurate numerical results of hydrodynamic loads based on the potential-flow theory is very challenging for structures with sharp edges, due to the singular behavior of the local-flow velocities. In this paper, we introduce the…
We propose an accurate and energy-stable parametric finite element method for solving the sharp-interface continuum model of solid-state dewetting in three-dimensional space. The model describes the motion of the film\slash vapor interface…
Graph-based methods have proven to be effective in capturing relationships among points for 3D point cloud analysis. However, these methods often suffer from suboptimal graph structures, particularly due to sparse connections at boundary…
In this study, we propose a parametric finite element method for a degenerate multi-phase Stefan problem with triple junctions. This model describes the energy-driven motion of a surface cluster whose distributional solution was studied by…
In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The…
Coarse grid projection (CGP) methodology is a novel multigrid method for systems involving decoupled nonlinear evolution equations and linear elliptic Poisson equations. The nonlinear equations are solved on a fine grid and the linear…
To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…
We develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a large number of applications in areas ranging from transport…
Constitutive models are fundamental to solid mechanics and materials science, underpinning the quantitative description and prediction of material responses under diverse loading conditions. Traditional phenomenological models, which are…
The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations.…
We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…
This work is devoted to the development of an efficient and robust technique for accurate capturing of the electric field in multi-material problems. The formulation is based on the finite element method enriched by the introduction of…
Active contour models based on local region fitting energy can segment images with intensity inhomogeneity effectively, but their segmentation results are easy to error if the initial contour is inappropriate. In this paper, we present a…
We propose numerical schemes for the approximate solution of problems defined on the edges of a one-dimensional graph. In particular, we consider linear transport and a drift-diffusion equations, and discretize them by extending Finite…