相关论文: Adaptive mesh refinement for conservative systems:…

High-resolution simulations often rely on the Adaptive Mesh Resolution (AMR) technique to optimize memory consumption versus attainable precision. While this technique allows for dramatic improvements in terms of computing performance, the…

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,…

There is great interest in numerical relativity simulations involving matter due to the likelihood that binary compact objects involving neutron stars will be detected by gravitational wave observatories in the coming years, as well as to…

We present the first high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multiple space dimensions. High order spatial accuracy is obtained through a WENO reconstruction, while a high order one-step…

Variational inequalities play a pivotal role in a wide array of scientific and engineering applications. This project presents two techniques for adaptive mesh refinement (AMR) in the context of variational inequalities, with a specific…

The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial…

Adaptive representations are increasingly indispensable for reducing the in-memory and on-disk footprints of large-scale data. Usual solutions are designed broadly along two themes: reducing data precision, e.g., through compression, or…

This work presents a high-order finite-difference adaptive mesh refinement (AMR) framework for robust simulation of shock-turbulence interaction problems. A staggered-grid arrangement, in which solution points are stored at cell centers…

Adaptive mesh refinement (AMR) is often used when solving time-dependent partial differential equations using numerical methods. It enables time-varying regions of much higher resolution, which can be used to track discontinuities in the…

Many physical problems involve spatial and temporal inhomogeneities that require a very fine discretization in order to be accurately simulated. Using an adaptive mesh, a high level of resolution is used in the appropriate areas while…

We compare two different codes for simulations of cosmological structure formation to investigate the sensitivity of hydrodynamical instabilities to numerics, in particular, the hydro solver and the application of adaptive mesh refinement…

The study of our Sun holds significant importance in Space Weather research, encompassing a diverse range of phenomena characterized by distinct temporal and spatial scales. To address these complexities, we developed CAFE-AMR, an…

Multi-resolution methods such as Adaptive Mesh Refinement (AMR) can enhance storage efficiency for HPC applications generating vast volumes of data. However, their applicability is limited and cannot be universally deployed across all…

The relativistic hydrodynamics (RHD) equations can give rise to solutions which have shocks, contact discontinuities, and other sharp structures, which interact and evolve over time. Capturing these sharp waves effectively requires a mesh…

Computationally solving the equations of elasticity is a key component in many materials science and mechanics simulations. Phenomena such as deformation-induced microstructure evolution, microfracture, and microvoid nucleation are examples…

Accurately and efficiently simulating complex fluid dynamics is a challenging task that has traditionally relied on computationally intensive methods. Neural network-based approaches, such as convolutional and graph neural networks, have…

Efforts to achieve better accuracy in numerical relativity have so far focused either on implementing second order accurate adaptive mesh refinement or on defining higher order accurate differences and update schemes. Here, we argue for the…

We present a fourth-order projection method with adaptive mesh refinement (AMR) for numerically solving the incompressible Navier-Stokes equations (INSE) with subcycling in time. Our method features (i) a reformulation of INSE so that the…

We introduce DynAMO, a reinforcement learning paradigm for Dynamic Anticipatory Mesh Optimization. Adaptive mesh refinement is an effective tool for optimizing computational cost and solution accuracy in numerical methods for partial…

The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution…