相关论文: A note on devising HDG+ projections on polyhedral …

Searching for numerical methods that combine facility and efficiency, while remaining accurate and versatile, is critical. Often, irregular geometries challenge traditional methods that rely on structured or body-fitted meshes. Meshless…

This paper presents a novel approach for the differentiable rendering of convex polyhedra, addressing the limitations of recent methods that rely on implicit field supervision. Our technique introduces a strategy that combines…

We define a new class of orthogonal polyhedra, called orthogrids, that can be unfolded without overlap with constant refinement of the gridded surface.

Illumination of scenes is usually generated in computer graphics using polygonal meshes. In this paper, we present a geometric method using projections. Starting from an implicit polynomial equation of a surface in 3-D or a curve in 2-D, we…

The Helmholtz-Hodge decomposition (HHD) is applied to the construction of Lyapunov functions. It is shown that if a stability condition is satisfied, such a decomposition can be chosen so that its potential function is a Lyapunov function.…

We present a scalable iterative solver for high-order hybridized discontinuous Galerkin (HDG) discretizations of linear partial differential equations. It is an interplay between domain decomposition methods and HDG discretizations, and…

When numerically solving partial differential equations (PDEs), the first step is often to discretize the geometry using a mesh and to solve a corresponding discretization of the PDE. Standard finite and spectral element methods require…

Revisiting the old problem of existence of interacting models of QFT with new conceptual ideas and mathematical tools, one arrives at a novel view about the nature of QFT. The recent success of algebraic methods in establishing the…

Many quantities we are interested in predicting are geometric tensors; we refer to this class of problems as geometric prediction. Attempts to perform geometric prediction in real-world scenarios have been limited to approximating them…

In this paper, we introduce new stable mixed finite elements of any order on polytopal mesh for solving second order elliptic problem. We establish optimal order error estimates for velocity and super convergence for pressure. Numerical…

This paper presents a novel multi-scale method for elliptic partial differential equations with arbitrarily rough coefficients. In the spirit of numerical homogenization, the method constructs problem-adapted ansatz spaces with uniform…

We construct a family of PL triangulations of the $d$-dimensional real projective space $\mathbb{R}P^d$ on $\Theta((\frac{1+\sqrt{5}}{2})^{d+1})$ vertices for every $d\geq 1$. This improves a construction due to K\"{u}hnel on $2^{d+1}-1$…

Using nonlinear projections and preserving structure in model order reduction (MOR) are currently active research fields. In this paper, we provide a novel differential geometric framework for model reduction on smooth manifolds, which…

A general method is introduced for constructing two-dimensional (2D) surface meshes embedded in three-dimensional (3D) space time, and 3D hypersurface meshes embedded in four-dimensional (4D) space time. In particular, we begin by dividing…

For any smooth projective variety with holomorphic locally homogeneous structure modelled on a homogeneous algebraic variety, we determine all the subvarieties of it which develop to the model.

We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough…

This paper discusses predictive inference and feature selection for generalized linear models with scarce but high-dimensional data. We argue that in many cases one can benefit from a decision theoretically justified two-stage approach:…

We develop projection operators onto finite element differential forms over simplicial meshes. Our projection is locally bounded in Lebesgue and Sobolev-Slobodeckij norms, uniformly with respect to mesh parameters. Moreover, it incorporates…

Due to its rich structure and close connection with gauge theory, hyperk\"ahler manifolds have attracted increasing interest. Using infinite dimensional hyperk\"ahler reduction, Kronheimer proved that certain adjoint orbits of complexified…

Algebraic hypergeometric functions can be compactly expressed as radical or dihedral functions on pull-back curves where the monodromy group is much simpler. This article considers the classical 3F2-functions with the projective monodromy…