相关论文: Adaptive Mesh Refinement for arbitrary initial Tri…

An extension of the framework of the Finite Integration Technique (FIT) including dynamic and adaptive mesh refinement is presented. After recalling the standard formulation of the FIT, the proposed mesh adaptation procedure is described.…

Adaptive Finite Element Method (adaptivity) is known to be an effective numerical tool for some ill-posed problems. The key advantage of the adaptivity is the image improvement with local mesh refinements. A rigorous proof of this property…

This work introduces an Adaptive Mesh Refinement (AMR) strategy for the topology optimization of structures made of discrete geometric components using the geometry projection method. Practical structures made of geometric shapes such as…

We introduce a smoothing algorithm for triangle, quadrilateral, tetrahedral and hexahedral meshes whose centerpiece is a simple geometric triangle transformation. The first part focuses on the mathematical properties of the element…

We present a novel algorithm to compute multi-scale curvature fields on triangle meshes. Our algorithm is based on finding robust mean curvatures using the ball neighborhood, where the radius of a ball corresponds to the scale of the…

We present an adaptive regularization algorithm that can be effectively applied to the optimization problem in deep learning framework. Our regularization algorithm aims to take into account the fitness of data to the current state of model…

A macro-constitutive model for the deformation response of periodic rotating bistable auxetic surfaces is developed. Focus is placed on isotropic surfaces made of bistable hexagonal cells composed of six triangular units with two stable…

We consider the problem of the construction of the acoustic structure of arbitrary geometry with prescribed desired properties. We use optimization approach for the solution of this problem and minimize the Tikhonov functional on adaptively…

Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…

The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In…

We present a modification to the Berger and Oliger adaptive mesh refinement algorithm designed to solve systems of coupled, non-linear, hyperbolic and elliptic partial differential equations. Such systems typically arise during constrained…

Full interpretation of data from gravitational wave observations will require accurate numerical simulations of source systems, particularly binary black hole mergers. A leading approach to improving accuracy in numerical relativity…

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…

The notions of discrete conformality on triangle meshes have rich mathematical theories and wide applications. The related notions of discrete uniformizations on triangle meshes, suggest efficient methods for computing the uniformizations…

We present a simple and efficient MATLAB implementation of the local refinement for polygonal meshes. The purpose of this implementation is primarily educational, especially on the teaching of adaptive virtual element methods.

We analyze adaptive mesh-refining algorithms for conforming finite element discretizations of certain non-linear second-order partial differential equations. We allow continuous polynomials of arbitrary, but fixed polynomial order. The…

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 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…

The numerical properties of algorithms for finding the intersection of sets depend to some extent on the regularity of the sets, but even more importantly on the regularity of the intersection. The alternating projection algorithm of von…

We present here the first systematic treatment of the problems posed by the visualization and analysis of large-scale, parallel adaptive mesh refinement (AMR) simulations on an Eulerian grid. When compared to those obtained by constructing…