相关论文: An exact general remeshing scheme applied to physi…

We introduce a fast and robust algorithm for finding a plane $\Gamma$ with given normal $\vec{n}_\Gamma$, which truncates an arbitrary polyhedron $\mathcal{P}$ such that the remaining sub-polyhedron admits a given volume…

In pure integer linear programming it is often desirable to work with polyhedra that are full-dimensional, and it is well known that it is possible to reduce any polyhedron to a full-dimensional one in polynomial time. More precisely, using…

In this paper, a second-order accurate method was developed for calculating fluid flows in complex geometries. This method uses cut-Cartesian cell mesh in finite volume framework. Calculus is employed to relate fluxes and gradients along…

Polytopal methods provide a flexible framework for the numerical approximation of partial differential equations on general meshes. Their convergence analysis raises specific challenges due to their inherently non-conforming nature and, in…

It is well-known that the convex and concave envelope of a multilinear polynomial over a box are polyhedral functions. Exponential-sized extended and projected formulations for these envelopes are also known. We consider the convexification…

A prerequisite for many biomechanical simulation techniques is discretizing a bounded volume into a tetrahedral mesh. In certain contexts, such as cortical surface simulations, preserving input surface connectivity is critical. However,…

We consider the problem of approximating partition functions for Ising models. We make use of recent tools in combinatorial optimization: the Sherali-Adams and Lasserre convex programming hierarchies, in combination with variational methods…

This research provides algorithms and numerical methods to geometrically control the magnitude of the internal and external forces in the reciprocal diagrams of 3D/Polyhedral Graphic statics (3DGS). In 3DGS, the form of the structure and…

This paper contains construction and analysis a finite element approximation for convection dominated diffusion problems with full coefficient matrix on general simplicial partitions in $R^d$, $d=2,3$. This construction is quite close to…

A new scheme for numerical integration of the 1D2V relativistic Vlasov-Maxwell system is proposed. Assuming that all particles in a cell of the phase space move with the same velocity as that of the particle located at the center of the…

This paper is concerned with inserting three-dimensional computer-aided design (CAD) geometries into meshes composed of hexahedral elements using a volume fraction representation. An adaptive procedure for doing so is presented. The…

In this work, we provide the first practical evaluation of the structural rounding framework for approximation algorithms. Structural rounding works by first editing to a well-structured class, efficiently solving the edited instance, and…

3D shape analysis is an important research topic in computer vision and graphics. While existing methods have generalized image-based deep learning to meshes using graph-based convolutions, the lack of an effective pooling operation…

The virtual element method (VEM) is a stabilized Galerkin method that is robust and accurate on general polygonal meshes. This feature makes it an appealing candidate for simulations involving meshes with embedded interfaces and evolving…

We introduce \emph{ReMatching}, a novel shape correspondence solution based on the functional maps framework. Our method, by exploiting a new and appropriate \emph{re}-meshing paradigm, can target shape-\emph{matching} tasks even on meshes…

Deterministic global optimization of nonlinear models is important in many scientific and engineering applications. This framework typically involves repeatedly solving convex relaxations of the nonconvex problem, meaning that the strength…

In this paper we introduce three complementary three-dimensional weighted quadratic enrichment strategies to improve the accuracy of local histopolation on tetrahedral meshes. The first combines face and interior weighted moments…

We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be…

The real radical ideal of a system of polynomials with finitely many complex roots is generated by a system of real polynomials having only real roots and free of multiplicities. It is a central object in computational real algebraic…

Incremental scene reconstruction is essential to the navigation in robotics. Most of the conventional methods typically make use of either TSDF (truncated signed distance functions) volume or neural networks to implicitly represent the…