Related papers: Afivo: a framework for quadtree/octree AMR with sh…
In an effort to study the applicability of adaptive mesh refinement (AMR) techniques to atmospheric models an interpolation-based spectral element shallow water model on a cubed-sphere grid is compared to a block-structured finite volume…
Recent advances in Neural Radiance Fields (NeRF) have demonstrated significant potential for representing 3D scene appearances as implicit neural networks, enabling the synthesis of high-fidelity novel views. However, the lengthy training…
This letter introduces DiffAero, a lightweight, GPU-accelerated, and fully differentiable simulation framework designed for efficient quadrotor control policy learning. DiffAero supports both environment-level and agent-level parallelism…
Partial differential equations (PDEs) with near singular solutions pose significant challenges for traditional numerical methods, particularly in complex geometries where mesh generation and adaptive refinement become computationally…
A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and…
We present here the first systematic treatment of the problems posed by the visualization and analysis of large-scale, parallel adaptive mesh refinement (AMR) simulations on an Eulerian grid. When compared to those obtained by constructing…
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…
Current AMR simulations require algorithms that are highly parallelized and manage memory efficiently. As compute engines grow larger, AMR simulations will require algorithms that achieve new levels of efficient parallelization and memory…
The forest-of-refinement-trees approach allows for dynamic adaptive mesh refinement (AMR) at negligible cost. While originally developed for quadrilateral and hexahedral elements, previous work established the theory and algorithms for…
An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…
We present a structure-aware parallel presolve framework specialized to arrowhead linear programs (AHLPs) and designed for high-performance computing (HPC) environments, integrated into the parallel interior point solver PIPS-IPM++.…
Vision transformers have delivered tremendous success in representation learning. This is primarily due to effective token mixing through self attention. However, this scales quadratically with the number of pixels, which becomes infeasible…
This article presents MuMFiM, an open source application for multiscale modeling of fibrous materials on massively parallel computers. MuMFiM uses two scales to represent fibrous materials such as biological network materials (extracellular…
In this work, we propose an adaptive geometric multigrid method for the solution of large-scale finite cell flow problems. The finite cell method seeks to circumvent the need for a boundary-conforming mesh through the embedding of the…
Miller and Reif's FOCS'85 classic and fundamental tree contraction algorithm is a broadly applicable technique for the parallel solution of a large number of tree problems. Additionally it is also used as an algorithmic design technique for…
In this work we formally derive and prove the correctness of the algorithms and data structures in a parallel, distributed-memory, generic finite element framework that supports h-adaptivity on computational domains represented as…
Bilevel optimization is a popular hierarchical model in machine learning, and has been widely applied to many machine learning tasks such as meta learning, hyperparameter learning and policy optimization. Although many bilevel optimization…
Fluid-structure interaction (FSI) simulation of biological systems presents significant computational challenges, particularly for applications involving large structural deformations and contact mechanics, such as heart valve dynamics.…
We present the derivation, implementation, and analysis of a multiresolution adaptive grid framework for numerical simulations on octree-based 3D block-structured collocated grids with distributed computational architectures. Our approach…
The development of novel materials in recent years has been accelerated greatly by the use of computational modelling techniques aimed at elucidating the complex physics controlling microstructure formation in materials, the properties of…