Related papers: Implementation of Polygonal Mesh Refinement in MAT…
We present a GPU-native mesh adaptation procedure that incorporates a complex geometry represented with a triangle mesh within a primary Cartesian computational grid organized as a forest of octrees. A C++/CUDA program implements the…
Certain Petrov-Galerkin schemes are inherently stable formulations of variational problems on a given mesh. This stability is primarily obtained by computing an optimal test basis for a given approximation space. Furthermore, these…
The $\ell$FEM MATLAB package provides a simple, efficient, and flexible implementation of isoparametric finite elements in bulk domains and on surfaces. The finite element matrix assemblies are based on MATLAB's paged operators and…
While 3D reconstruction is a well-established and widely explored research topic, semantic 3D reconstruction has only recently witnessed an increasing share of attention from the Computer Vision community. Semantic annotations allow in fact…
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…
The present work deals with the formulation of a Virtual Element Method (VEM) for two dimensional structural problems. The contribution is split in two parts: in part I, the elastic problem is discussed, while in part II [3] the method is…
In this paper we analyze a virtual element method for the two dimensional elasticity problem allowing small edges. With this approach, the classic assumptions on the geometrical features of the polygonal meshes can be relaxed. In…
We discuss adaptive mesh point selection for the solution of scalar IVPs. We consider a method that is optimal in the sense of the speed of convergence, and aim at minimizing the local errors. Although the speed of convergence cannot be…
As an important metric for mesh quality evaluation, the isotropy property holds significant value for applications such as texture UV-mapping, physical simulation, and discrete geometric analysis. Classical isotropy remeshing methods adjust…
We design an adaptive finite element method to approximate the solutions of quasi-linear elliptic problems. The algorithm is based on a Ka\v{c}anov iteration and a mesh adaptation step is performed after each linear solve. The method is…
With the recent advances in hardware and rendering techniques, 3D models have emerged everywhere in our life. Yet creating 3D shapes is arduous and requires significant professional knowledge. Meanwhile, Deep learning has enabled…
Mesh adaption procedures for finite element approximation allows one to adapt the resolution, by local refinement in the regions of strong variation of the function of interest. This procedure plays a key role in numerous applications of…
For modeling the 3D world behind 2D images, which 3D representation is most appropriate? A polygon mesh is a promising candidate for its compactness and geometric properties. However, it is not straightforward to model a polygon mesh from…
Finite elements of higher continuity, say conforming in $H^2$ instead of $H^1$, require a mapping from reference cells to mesh cells which is continuously differentiable across cell interfaces. In this article, we propose an algorithm to…
In this work, we describe a simple finite element approach that is able to resolve weak discontinuities in interface problems accurately. The approach is based on a fixed patch mesh consisting of quadrilaterals, that will stay unchanged…
The use of adaptive mesh refinement (AMR) techniques is crucial for accurate and efficient simulation of higher dimensional spacetimes. In this work we develop an adaptive algorithm tailored to the integration of finite difference…
Automatic color enhancement is aimed to adaptively adjust photos to expected styles and tones. For current learned methods in this field, global harmonious perception and local details are hard to be well-considered in a single model…
Convergence failure and slow convergence rates are among the biggest challenges with solving the system of non-linear equations numerically. Although mitigated, such issues still linger when using strictly small time steps and…
Depth maps are used in a wide range of applications from 3D rendering to 2D image effects such as Bokeh. However, those predicted by single image depth estimation (SIDE) models often fail to capture isolated holes in objects and/or have…
Despite having achieved real-time performance in mesh construction, most of the current LiDAR odometry and meshing methods may struggle to deal with complex scenes due to relying on explicit meshing schemes. They are usually sensitive to…