Related papers: Efficient and Global Optimization-Based Smoothing …
We introduce a class of stochastic algorithms for minimizing weakly convex functions over proximally smooth sets. As their main building blocks, the algorithms use simplified models of the objective function and the constraint set, along…
It is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization process towards local (and non-physical) minima, and by the…
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing on the refined part of the mesh. Partitioning is achieved by…
Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the variational framework introduced in Wibisono et al. In this…
Although the isogeometric analysis has shown its great potential in achieving highly accurate numerical solutions of partial differential equations, its efficiency is the main factor making the method more competitive in practical…
We develop an all-hex meshing strategy for the interstitial space in beds of densely packed spheres that is tailored to turbulent flow simulations based on the spectral element method (SEM). The SEM achieves resolution through elevated…
In this paper, we present a surface remeshing method with high approximation quality based on Principal Component Analysis. Given a triangular mesh and a user assigned polygon/vertex budget, traditional methods usually require the extra…
We propose a new approach for controlling the characteristics of certain mesh faces during optimization of high-order curved meshes. The practical goals are tangential relaxation along initially aligned curved boundaries and internal…
We propose a method that morphs high-orger meshes such that their boundaries and interfaces coincide/align with implicitly defined geometries. Our focus is particularly on the case when the target surface is prescribed as the zero…
Skinning is a popular way to rig and deform characters for animation, to compute reduced-order simulations, and to define features for geometry processing. Methods built on skinning rely on weight functions that distribute the influence of…
We consider a class of nonsmooth and nonconvex optimization problems over the Stiefel manifold where the objective function is the summation of a nonconvex smooth function and a nonsmooth Lipschitz continuous convex function composed with…
This work studies three multigrid variants for matrix-free finite-element computations on locally refined meshes: geometric local smoothing, geometric global coarsening, and polynomial global coarsening. We have integrated the algorithms…
Mesh denoising is a fundamental problem in digital geometry processing. It seeks to remove surface noise, while preserving surface intrinsic signals as accurately as possible. While the traditional wisdom has been built upon specialized…
Mesh simplification is the process of reducing the number of vertices, edges and triangles in a three-dimensional (3D) mesh while preserving the overall shape and salient features of the mesh. A popular strategy for this is edge collapse,…
This paper examines a variety of classical optimization problems, including well-known minimization tasks and more general variational inequalities. We consider a stochastic formulation of these problems, and unlike most previous work, we…
The problem of polycube construction or deformation is an essential problem in computer graphics. In this paper, we present a robust, simple, efficient and automatic algorithm to deform the meshes of arbitrary shapes into their polycube…
Recent developments for mathematical modeling and numerical simulation of biomolecular systems raise new demands for qualified, stable, and efficient surface meshing, especially in implicit-solvent modeling. In our former work, we have…
Geometry optimization is an important task in quantum chemical calculations to analyze the characteristics of molecules. A top concern on it is a long execution time because time-consuming energy and gradient calculations are repeated…
The convergence of multigrid methods degrades significantly if a small number of low quality cells are present in a finite element mesh, and this can be a barrier to the efficient and robust application of multigrid on complicated geometric…
Reconstructing real-world objects from multi-view images is essential for applications in 3D editing, AR/VR, and digital content creation. Existing methods typically prioritize either geometric accuracy (Multi-View Stereo) or photorealistic…