Related papers: Accelerating High-Order Mesh Optimization Using Fi…
CPU-GPU heterogeneous systems are now commonly used in HPC (High-Performance Computing). However, improving the utilization and energy-efficiency of such systems is still one of the most critical issues. As one single program typically…
In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…
Adaptive finite elements combined with geometric multigrid solvers are one of the most efficient numerical methods for problems such as the instationary Navier-Stokes equations. Yet despite their efficiency, computations remain expensive…
This paper presents a highly efficient method to obtain high-resolution, near-optimal 3D topologies optimized for minimum compliance on a standard PC. Using an implicit geometry description we derive a single-scale interpretation of optimal…
We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into…
The so-called matrix-element method (MEM) has long been used successfully as a classification tool in particle physics searches. In the presence of invisible final state particles, the traditional MEM typically assigns probabilities to an…
The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convex problems that has received renewed interest over the last decade. Despite its popularity, very little is known in terms…
Motion planning is a key aspect of robotics. A common approach to address motion planning problems is trajectory optimization. Trajectory optimization can represent the high-level behaviors of robots through mathematical formulations.…
We present numerical experiments for geophysics electromagnetic (EM) modeling based upon high-order edge elements and supervised $h+p$ refinement approaches on massively parallel computers. Our high-order $h+p$ refinement strategy is based…
Finite element model updating of a structure made of linear elastic materials is based on the solution of a minimization problem. The goal is to find some unknown parameters of the finite element model (elastic moduli, mass densities,…
Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the domain limits the accuracy of finite element methods based on…
This article addresses the research question if and how the finite cell method, an embedded domain finite element method of high order, may be used in the simulation of metal deposition to harvest its computational efficiency. This…
We present an efficient B-spline finite element method (FEM) for cloth simulation. While higher-order FEM has long promised higher accuracy, its adoption in cloth simulators has been limited by its larger computational costs while…
We provide improved convergence rates for various \emph{non-smooth} optimization problems via higher-order accelerated methods. In the case of $\ell_\infty$ regression, we achieves an $O(\epsilon^{-4/5})$ iteration complexity, breaking the…
Branch-and-Bound (B&B) algorithms are time intensive tree-based exploration methods for solving to optimality combinatorial optimization problems. In this paper, we investigate the use of GPU computing as a major complementary way to speed…
This paper presents a novel p-adaptive, high-order mesh-free framework for the accurate and efficient simulation of fluid flows in complex geometries. High-order differential operators are constructed locally for arbitrary node…
This paper introduces a warehouse optimization procedure aimed at enhancing the efficiency of product storage and retrieval. By representing product locations and order flows within a time-evolving graph structure, we employ unsupervised…
A higher-order accurate finite element method is proposed which uses automatically generated meshes based on implicit level-set data for the description of boundaries and interfaces in two and three dimensions. The method is an alternative…
Sparse matrix-vector multiplication (SpMV) is a fundamental operation with a wide range of applications in scientific computing and artificial intelligence. However, the large scale and sparsity of sparse matrix often make it a performance…
We analyze optimal complexity of adaptive finite element methods (AFEMs) for general second-order linear elliptic partial differential equations (PDEs) in the Lax-Milgram setting. To this end, we formulate an adaptive algorithm which steers…