相关论文: Anisotropic mesh adaptation in Firedrake with PETS…

A common approach for generating an anisotropic mesh is the M-uniform mesh approach where an adaptive mesh is generated as a uniform one in the metric specified by a given tensor M. A key component is the determination of an appropriate…

Efficient and robust anisotropic mesh adaptation is crucial for Computational Fluid Dynamics (CFD) simulations. The CFD Vision 2030 Study highlights the pressing need for this technology, particularly for simulations targeting…

We consider problems related to initial meshing and adaptive mesh refinement for the electromagnetic simulation of various structures. The quality of the initial mesh and the performance of the adaptive refinement are of great importance…

Anisotropic Porous Medium Equation (APME) is developed as an extension of the Porous Medium Equation (PME) for anisotropic porous media. A special analytical solution is derived for APME for time-independent diffusion. Anisotropic mesh…

As an important metric for mesh quality evaluation, the isotropy property holds significant value for applications such as texture UV-mapping, physical simulation, and discrete geometric analysis. Classical isotropy remeshing methods adjust…

We present a novel approach to automate and optimize anisotropic p-adaptation in high-order h/p solvers using Reinforcement Learning (RL). The dynamic RL adaptation uses the evolving solution to adjust the high-order polynomials. We develop…

Simplifying complex 3D meshes is a crucial step in robotics applications to enable efficient motion planning and physics simulation. Common methods, such as approximate convex decomposition, represent a mesh as a collection of simple parts,…

Firedrake is a new tool for automating the numerical solution of partial differential equations. Firedrake adopts the domain-specific language for the finite element method of the FEniCS project, but with a pure Python runtime-only…

Radiative transfer is a notoriously difficult and computationally demanding problem. Yet, it is an indispensable ingredient in nearly all astrophysical and cosmological simulations. Choosing an appropriate discretization scheme is a crucial…

Non-uniform grids and mesh adaptation have been a growing part of numerical simulation over the past years. It has been experimentally noted that mesh adaptation leads not only to locally improved solution but also to numerical stability of…

We propose a novel multimesh rational approximation scheme for the numerical solution of the (homogeneous) Dirichlet problem for the spectral fractional Laplacian. The scheme combines a rational approximation of the function $\lambda…

Data-driven methods have shown great potential in solving challenging manipulation tasks; however, their application in the domain of deformable objects has been constrained, in part, by the lack of data. To address this lack, we propose…

This article describes a new, fully adaptive Particle-Multiple-Mesh numerical simulation code developed primarily for simulations of small regions (such as a group of galaxies) in a cosmological context. It integrates the equations of…

Adaptive meshing includes local refinement as well as coarsening of meshes. Typically, coarsening algorithms are based on an explicit refinement history. In this work, we deal with local coarsening algorithms that build on the refinement…

This article presents a hardware architecture independent implementation of an adaptive mesh refinement Poisson solver that is integrated into the electrostatic Particle-In-Cell beam dynamics code OPAL. The Poisson solver is solely based on…

Consider the Poisson equation with the Dirichlet boundary condition on a three-dimensional polyhedral domain. For singular solutions from the non-smoothness of the domain boundary, we propose new anisotropic tetrahedral mesh refinement…

The implementation process of a $\texttt{RestrictedFunctionSpace}$ class in Firedrake, a Python library which numerically solves partial differential equations through the use of the finite element method, is documented. This includes an…

Simulating physical systems is essential in engineering, but analytical solutions are limited to straightforward problems. Consequently, numerical methods like the Finite Element Method (FEM) are widely used. However, the FEM becomes…

Parallel implementation of numerical adaptive mesh refinement (AMR)strategies for solving 3D elastostatic contact mechanics problems is an essential step toward complex simulations that exceed current performance levels. This paper…

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…