Scalable Algorithms for Parallel Tree-based Adaptive Mesh Refinement with General Element Types

TL;DR

This thesis presents scalable parallel algorithms for adaptive mesh refinement that are independent of element type, utilizing space-filling curves and introducing a new tetrahedral Morton index for simplices.

Contribution

It introduces a general, scalable AMR software framework with a novel tetrahedral Morton index, enabling efficient refinement across various element types.

Findings

Developed a new tetrahedral Morton index (TM-index) for simplices.

Created a flexible, scalable AMR software applicable to multiple element types.

Validated scalability on supercomputers with different element geometries.

Abstract

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, such as for example lines, triangles, tetrahedra, quadrilaterals, hexahedra, and prisms. Along with a detailed mathematical discussion, this requires the implementation as a numerical software and its validation, as well as scalability tests on current supercomputers. For triangular and tetrahedral elements (simplices) with red-refinement (1:4 in 2D, 1:8 in 3D), we develop a new SFC index, the tetrahedral Morton index (TM-index). Its construction is similar to the Morton index for quadrilaterals/hexahedra, as it is also based on bitwise interleaving the coordinates of a certain vertex of the simplex, the anchor node. We develop and demonstrate a new simplicial SFC and create a fast and scalable tree-based AMR software that offers a flexibility and generality that was previously not available.