相关论文: Isogeometric Analysis on V-reps: first results

We consider the vertex-centered finite volume method with first-order conforming ansatz functions. The adaptive mesh-refinement is driven by the local contributions of the weighted-residual error estimator. We prove that the adaptive…

Polycube-maps are used as base-complexes in various fields of computational geometry, including the generation of regular all-hexahedral meshes free of internal singularities. However, the strict alignment constraints behind polycube-based…

In the burgeoning field of medical imaging, precise computation of 3D volume holds a significant importance for subsequent qualitative analysis of 3D reconstructed objects. Combining multivariate calculus, marching cube algorithm, and…

Dimensionality reduction algorithms map high-dimensional data into visualizable 2D or 3D spaces, but traditionally rely on a discrete point-cloud paradigm. This discrete abstraction is susceptible to visual occlusion and artificial…

We represent an algorithm allowing one to construct new classes of partially integrable multidimensional nonlinear partial differential equations (PDEs) starting with the special type of solutions to the (1+1)-dimensional hierarchy of…

In this work, we propose the application of the eXtended Finite Element Method (XFEM) in the context of the coupling between three-dimensional and one-dimensional elliptic problems. In particular, we consider the case in which the 3D-1D…

We introduce a novel neural operator architecture designed to approximate solutions of linear elliptic partial differential equations with high-contrast, spatially varying coefficients. The network, termed the Iterated V-shaped Net…

We present a novel method for solving high-order partial differential equations (PDEs) over planar multi-patch geometries demonstrated on the basis of the polyharmonic equation of order $m$, $m \geq 1$, which is a particular linear elliptic…

In this paper we present a new method, which allows for the construction of triangular isosurfaces from three-dimensional data sets, such as 3D image data and/or numerical simulation data that are based on regularly shaped, cubic lattices.…

We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is…

We present a collection of algorithms which utilize dimensional reduction to perform mesh refinement and study possibly singular solutions of time-dependent partial differential equations. The algorithms are inspired by constructions used…

We consider isomonodromic deformations of connections with a simple pole on the torus, motivated by the elliptic version of the sixth Painlev\'e equation. We establish an extended symmetry, complementing known results. The Calogero-Moser…

This work introduces IsUMap, a novel manifold learning technique that enhances data representation by integrating aspects of UMAP and Isomap with Vietoris-Rips filtrations. We present a systematic and detailed construction of a metric…

In this work we analyze a virtual element method on polyhedral meshes for solving the sixth-order elliptic problem with simply supported boundary conditions. We apply the Ciarlet-Raviart arguments to introduce an auxiliary unknown…

Given an arbitrary set of high dimensional points in $\ell_1$, there are known negative results that preclude the possibility of always mapping them to a low dimensional $\ell_1$ space while preserving distances with small multiplicative…

We derive aposteriori error estimates for fully discrete approximations to solutions of linear parabolic equations on the space-time domain. The space discretization uses finite element spaces, that are allowed to change in time. Our main…

In this paper, we introduce a multiscale framework based on adaptive edge basis functions to solve second-order linear elliptic PDEs with rough coefficients. One of the main results is that we prove the proposed multiscale method achieves…

We study flexible polyhedral nets in isotropic geometry. This geometry has a degenerate metric, but there is a natural notion of flexibility. We study infinitesimal and finite flexibility, and classify all finitely flexible polyhedral nets…

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…

Reconstructing three-dimensional (3D) scenes with semantic understanding is vital in many robotic applications. Robots need to identify which objects, along with their positions and shapes, to manipulate them precisely with given tasks.…