Related papers: Local Coarsening Algorithms on Adaptively Refined …

In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…

This chapter provides an overview of state-of-the-art adaptive finite element methods (AFEMs) for the numerical solution of second-order elliptic partial differential equations (PDEs), where the primary focus is on the optimal interplay of…

Triangular meshes are a widely used representation in the field of 3D modeling. In this paper, we present a novel approach for edge length-based linear subdivision on triangular meshes, along with two auxiliary techniques. We conduct a…

This is a survey on the theory of adaptive finite element methods (AFEMs), which are fundamental in modern computational science and engineering but whose mathematical assessment is a formidable challenge. We present a self-contained and…

Neural Radiance Fields (NeRF) have constituted a remarkable breakthrough in image-based 3D reconstruction. However, their implicit volumetric representations differ significantly from the widely-adopted polygonal meshes and lack support…

Adaptivity and local mesh refinement are crucial for the efficient numerical simulation of wave phenomena in complex geometry. Local mesh refinement, however, can impose a tiny time-step across the entire computational domain when using…

Adaptive mesh refinement (AMR) is indispensable for efficient finite element analyses. However, its performance depends not only on the refinement itself but also on strategy to mark elements for refinement and the way it is tuned. This…

Finding coarse representations of large graphs is an important computational problem in the fields of scientific computing, large scale graph partitioning, and the reduction of geometric meshes. Of particular interest in all of these fields…

This work is focused on the extension and assessment of the monotonicity-preserving scheme in [3] and the local bounds preserving scheme in [5] to hierarchical octree adaptive mesh refinement (AMR). Whereas the former can readily be used on…

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…

Finetuning on domain-specific data is a well-established method for enhancing LLM performance on downstream tasks. Training on each dataset produces a new set of model weights, resulting in a multitude of checkpoints saved in-house or on…

Reference-based super-resolution (RefSR) has made significant progress in producing realistic textures using an external reference (Ref) image. However, existing RefSR methods obtain high-quality correspondence matchings consuming quadratic…

We present a new method for performing Boolean operations on volumes represented as triangle meshes. In contrast to existing methods which treat meshes as 3D polyhedra and try to partition the faces at their exact intersection curves, we…

This work introduces a framework to address the computational complexity inherent in Mixed-Integer Programming (MIP) models by harnessing the potential of deep learning. By employing deep learning, we construct problem-specific heuristics…

Due to the wide range of timescales that are present in macromolecular systems, hierarchical multiscale strategies are necessary for their computational study. Coarse-graining (CG) allows to establish a link between different system…

In this paper, we investigate and design multiscale simulations for stochastic multiscale PDEs. As for the space, we consider a coarse grid and a known multiscale method, the Generalized Multiscale Finite Element Method (GMsFEM). In order…

Adaptive, locally refined and locally adjusted meshes are preferred over uniform meshes for capturing singular or localised solutions. Roughly speaking, for a given degree of freedom a solution associated with adaptive, locally refined and…

We present an adaptive refinement algorithm for T-splines on unstructured 2D meshes. While for structured 2D meshes, one can refine elements alternatingly in horizontal and vertical direction, such an approach cannot be generalized directly…

In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel scalable distributed-memory implementation of the resulting…

High-fidelity computational fluid dynamics (CFD) simulations for design space explorations can be exceedingly expensive due to the cost associated with resolving the finer scales. This computational cost/accuracy trade-off is a major…