Non-Conforming Mesh Refinement for High-Order Finite Elements
This work provides a flexible and scalable AMR framework for high-order finite element codes, addressing a key bottleneck in large-scale simulations.
The paper presents a general algorithm for non-conforming adaptive mesh refinement (AMR) for high-order finite elements, supporting various element types and arbitrary refinement ratios. The algorithm scales to billions of elements on 393,000 parallel tasks and is integrated into a high-order Lagrangian hydrodynamics solver.
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, quadrilateral, hexahedral and prismatic meshes of arbitrarily high order curvature, for any order finite element space in the de Rham sequence. We present a flexible data structure for meshes with hanging nodes and a general procedure to construct the conforming interpolation operator, both in serial and in parallel. The algorithm and data structure allow anisotropic refinement of tensor product elements in 2D and 3D, and support unlimited refinement ratios of adjacent elements. We report numerical experiments verifying the correctness of the algorithms, and perform a parallel scaling study to show that we can adapt meshes containing billions of elements and run efficiently on 393,000 parallel tasks. Finally, we illustrate the integration of dynamic AMR into a high-order Lagrangian hydrodynamics solver.