相关论文: Binarized octree generation for Cartesian adaptive…

Structured adaptive mesh refinement (AMR), commonly implemented via quadtrees and octrees, underpins a wide range of applications including databases, computer graphics, physics simulations, and machine learning. However, octrees enforce…

The forest-of-octrees approach to parallel adaptive mesh refinement and coarsening (AMR) has recently been demonstrated in the context of a number of large-scale PDE-based applications. Although linear octrees, which store only leaf…

Adaptive mesh refinement (AMR) is widely used to efficiently resolve localized features in time-dependent partial differential equations (PDEs) by selectively refining and coarsening the mesh. However, in long-horizon simulations, repeated…

In this thesis, we develop, discuss and implement algorithms for scalable parallel tree-based adaptive mesh refinement (AMR) using space-filling curves (SFCs). We create an AMR software that works independently of the used element type,…

I consider techniques for Berger-Oliger adaptive mesh refinement (AMR) when numerically solving partial differential equations with wave-like solutions, using characteristic (double-null) grids. Such AMR algorithms are naturally recursive,…

In tree based adaptive mesh refinement, elements are partitioned between processes using a space filling curve. The curve establishes an ordering between all elements that derive from the same root element, the tree. When representing more…

When introducing physics-constrained deep learning solutions to the volumetric super-resolution of scientific data, the training is challenging to converge and always time-consuming. We propose a new hierarchical sampling method based on…

We present a new hybrid paradigm for parallel adaptive mesh refinement (AMR) that combines the scalability and lightweight architecture of tree-based AMR with the computational efficiency of patch-based solvers for hyperbolic conservation…

Adaptive mesh refinement (AMR) reduces computational costs in CFD by concentrating resolution where needed, but efficiently embedding complex, non-aligned geometries on GPUs remains challenging. We present a GPU-native algorithm for…

We propose a general algorithm for non-conforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on h-refinement with a fixed polynomial order. The algorithm handles triangular,…

Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set…

In this article, we present a novel approach for block-structured adaptive mesh refinement (AMR) that is suitable for extreme-scale parallelism. All data structures are designed such that the size of the meta data in each distributed…

We present an MPI-parallel algorithm for the in-situ visualization of computational data that is built around a distributed linear forest-of-octrees data structure. Such octrees are frequently used in element-based numerical simulations;…

The paper develops a finite element method for partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method uses traces of bulk finite element functions on a surface embedded in a volumetric domain. The bulk…

We examine the effect of accuracy of high-order spectral element methods, with or without adaptive mesh refinement (AMR), in the context of a classical configuration of magnetic reconnection in two space dimensions, the so-called…

The initial data for black hole collisions is constructed using a conformal-imaging approach and a new adaptive mesh refinement technique, a fully threaded tree (FTT). We developed a second-order accurate approach to the solution of the…

Adaptive Mesh Refinement (AMR) enables efficient computation of flows by providing high resolution in critical regions while allowing for coarsening in areas where fine detail is unnecessary. While early AMR software packages relied solely…

We present a new software package, "HybridOctree_Hex," for adaptive all-hexahedral mesh generation based on hybrid octree and quality improvement with Jacobian control. The proposed HybridOctree_Hex begins by detecting curvatures and narrow…

We propose a new outline for adaptive dictionary learning methods for sparse encoding based on a hierarchical clustering of the training data. Through recursive application of a clustering method, the data is organized into a binary…

We observe that a standard transformation between \emph{ordinal} trees (arbitrary rooted trees with ordered children) and binary trees leads to interesting succinct binary tree representations. There are four symmetric versions of these…