Related papers: Stable Mesh Decimation
Mesh deformation plays a pivotal role in many 3D vision tasks including dynamic simulations, rendering, and reconstruction. However, defining an efficient discrepancy between predicted and target meshes remains an open problem. A prevalent…
In two-phase flow simulations, a difficult issue is usually the treatment of surface tension effects. These cause a pressure jump that is proportional to the curvature of the interface separating the two fluids. Since the evaluation of the…
We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the nonlinear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly…
We develop a conservative cut finite element method for an elliptic coupled bulk-interface problem. The method is based on a discontinuous Galerkin framework where stabilization is added in such a way that we retain conservation on macro…
In this work, we analyze an unfitted discontinuous Galerkin discretization for the numerical solution of the Stokes system based on equal higher-order discontinuous velocities and pressures. This approach combines the best from both worlds,…
Shape calculus concerns the calculation of directional derivatives of some quantity of interest, typically expressed as an integral. This article introduces a type of shape calculus based on localized dilation of boundary faces through…
Feature detection is an important procedure for image matching, where unsupervised feature detection methods are the detection approaches that have been mostly studied recently, including the ones that are based on repeatability requirement…
This paper presents a framework for the analysis of discretization methods based on the decomposition into local and global problems. We apply the framework to provide a comprehensive error analysis for the embedded Trefftz discontinuous…
Near-optimal computational complexity of an adaptive stochastic Galerkin method with independently refined spatial meshes for elliptic partial differential equations is shown. The method takes advantage of multilevel structure in expansions…
This work presents a novel surface decomposition method for the sensitivity analysis of first-passage dynamic reliability of linear systems subjected to Gaussian random excitations. The method decomposes the sensitivity of first-passage…
The moving mesh PDE (MMPDE) method for variational mesh generation and adaptation is studied theoretically at the discrete level, in particular the nonsingularity of the obtained meshes. Meshing functionals are discretized geometrically and…
We explore a vexing benchmark problem for viscoelastic fluid flows with the discontinuous Petrov-Galerkin (DPG) finite element method of Demkowicz and Gopalakrishnan [1,2]. In our analysis, we develop an intrinsic a posteriori error…
The rapidly evolving field of engineering design of functional surfaces necessitates sophisticated tools to manage the inherent complexity of high-dimensional design spaces. This survey paper offers a scoping review, i.e., a literature…
Partitioning a polygonal mesh into meaningful parts can be challenging. Many applications require decomposing such structures for further processing in computer graphics. In the last decade, several methods were proposed to tackle this…
In this work we present an a priori error analysis for solving the unsteady advection equation on cut cell meshes along a straight ramp in two dimensions. The space discretization uses a lowest order upwind-type discontinuous Galerkin…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
In recent work we have shown how an accurate reduced model can be utilized to perform mesh refinement in random space. That work relied on the explicit knowledge of an accurate reduced model which is used to monitor the transfer of activity…
Modern product design in the engineering domain is increasingly driven by computational analysis including finite-element based simulation, computational optimization, and modern data analysis techniques such as machine learning. To apply…
We investigate numerically a quasi-static elasticity system of Kachanov-type. To do so we propose an Euler time discretization combined with a suitable finite elements scheme (FEM) to handle the discretization is space. We use ODE-type…
In this paper, we propose a novel meshfree Generalized Finite Difference Method (GFDM) approach to discretize PDEs defined on manifolds. Derivative approximations for the same are done directly on the tangent space, in a manner that mimics…