Related papers: General Field Evaluation in High-Order Meshes on G…
This paper focuses on interior penalty discontinuous Galerkin methods for second order elliptic equations on very general polygonal or polyhedral meshes. The mesh can be composed of any polygons or polyhedra which satisfies certain shape…
The key task of physical simulation is to solve partial differential equations (PDEs) on discretized domains, which is known to be costly. In particular, high-fidelity solutions are much more expensive than low-fidelity ones. To reduce the…
We derive error estimates for the piecewise linear finite element approximation of the Laplace--Beltrami operator on a bounded, orientable, $C^3$, surface without boundary on general shape regular meshes. As an application, we consider a…
Acceleration of algorithms is becoming a crucial problem, if larger data sets are to be processed. Evaluation of algorithms is mostly done by using computational geometry approach and evaluation of computational complexity. However in…
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…
We consider families of finite elements on polygonal meshes, that are defined implicitly on each mesh cell as solutions of local Poisson problems with polynomial data. Functions in the local space on each mesh cell are evaluated via…
Estimating the trajectories of multi-objects poses a significant challenge due to data association ambiguity, which leads to a substantial increase in computational requirements. To address such problems, a divide-and-conquer manner has…
In this work, we present a general, efficient, and provably robust representation for intrinsic triangulations. These triangulations have emerged as a powerful tool for robust geometry processing of surface meshes, taking a low-quality mesh…
In this work, we propose a generalized multiscale inversion algorithm for heterogeneous problems that aims at solving an inverse problem on a computational coarse grid. Previous inversion techniques for multiscale problems seek a…
In this paper, we discuss the application of the Generalized Finite Element Method (GFEM) to approximate the solutions of quasilinear elliptic equations with multiple interfaces in one dimensional space. The problem is characterized by…
Mesh adaptivity is a useful tool for efficient solution to partial differential equations in very complex geometries. In the present paper we discuss the use of polygonal mesh refinement in order to tackle two common issues: first,…
Immersed finite element methods provide a convenient analysis framework for problems involving geometrically complex domains, such as those found in topology optimization and microstructures for engineered materials. However, their…
Localized features such as singularities, sharp gradients, discontinuities, and moving sources require adaptive finite element discretizations. Conventional refinement strategies introduce significant computational overhead through…
3D Gaussian Splatting (3DGS) has shown promising performance in novel view synthesis. Previous methods adapt it to obtaining surfaces of either individual 3D objects or within limited scenes. In this paper, we make the first attempt to…
We develop and test high-order methods for integration on surface point clouds. The task of integrating a function on a surface arises in a range of applications in engineering and the sciences, particularly those involving various integral…
Given a graphical model (GM), computing its partition function is the most essential inference task, but it is computationally intractable in general. To address the issue, iterative approximation algorithms exploring certain local…
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 Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which…
We present a computational scheme that derives a global polynomial level set parametrisation for smooth closed surfaces from a regular surface-point set and prove its uniqueness. This enables us to approximate a broad class of smooth…
We propose a general algorithm for non-conforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on h-refinement with a fixed polynomial order. The algorithm handles triangular,…