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Accurate modeling of complex physical problems, such as fluid-structure interaction, requires multiphysics coupling across the interface, which often has intricate geometry and dynamic boundaries. Conventional numerical methods face…

Computational Fluid Dynamics (CFD) is a major sub-field of engineering. Corresponding flow simulations are typically characterized by heavy computational resource requirements. Often, very fine and complex meshes are required to resolve…

In this paper, we propose a mesh-free method to solve interface problems using the deep learning approach. Two interface problems are considered. The first one is an elliptic PDE with a discontinuous and high-contrast coefficient. While the…

Computing the stiffness matrix for the finite element discretization of the nonlocal Laplacian on unstructured meshes is difficult, because the operator is nonlocal and can even be singular. In this paper, we focus on the $C^0$-piecewise…

Visual-Inertial Odometry (VIO) algorithms typically rely on a point cloud representation of the scene that does not model the topology of the environment. A 3D mesh instead offers a richer, yet lightweight, model. Nevertheless, building a…

Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a…

In this paper, we address the problem of automatic mesh generation for finite elements modeling of anatomical organs for which a volumetric data set is available. In the first step a set of characteristic outlines of the organ is defined…

Spatially localized deformation components are very useful for shape analysis and synthesis in 3D geometry processing. Several methods have recently been developed, with an aim to extract intuitive and interpretable deformation components.…

We develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in…

In this paper, we address a way to reduce the total computational cost of meshless approximation by reducing the required stencil size through spatially varying computational node regularity. Rather than covering the entire domain with…

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…

Directly generating 3D meshes, the default representation for 3D shapes in the graphics industry, using auto-regressive (AR) models has become popular these days, thanks to their sharpness, compactness in the generated results, and ability…

Thanks to a finite element method, we solve numerically parabolic partial differential equations on complex domains by avoiding the mesh generation, using a regular background mesh, not fitting the domain and its real boundary exactly. Our…

The finite element method (FEM) has several computational steps to numerically solve a particular problem, to which many efforts have been directed to accelerate the solution stage of the linear system of equations. However, the finite…

Metasurfaces have become a promising means for manipulating optical wavefronts in flat and high-performance optical devices. Conventional metasurface device design relies on trial-and-error methods to obtain target electromagnetic (EM)…

The quality of mesh generation has long been considered a vital aspect in providing engineers with reliable simulation results throughout the history of the Finite Element Method (FEM). The element extraction method, which is currently the…

The traditional algorithms do not meet the latest multiple requirements simultaneously for objects. Density-based method is one of the methodologies, which can detect arbitrary shaped clusters where clusters are defined as dense regions…

In this paper, we introduce the Phantom Domain Finite Element Method (PDFEM), a novel computational approach tailored for the efficient analysis of heterogeneous and composite materials. Inspired by fictitious domain methods, this method…

We introduce a generative learning framework to model high-dimensional parametric systems using gradient guidance and virtual observations. We consider systems described by Partial Differential Equations (PDEs) discretized with structured…

Many time-dependent problems in the field of computational fluid dynamics can be solved using space-time methods. However, such methods can encounter issues with computational cost and robustness. In order to address these issues,…