Coarse Mesh Partitioning for Tree-Based AMR

Abstract

In tree based adaptive mesh refinement, elements are partitioned between processes using a space filling curve. The curve establishes an ordering between all elements that derive from the same root element, the tree. When representing more complex geometries by patching together several trees, the roots of these trees form an unstructured coarse mesh. We present an algorithm to partition the elements of the coarse mesh such that (a) the fine mesh can be load-balanced to equal element counts per process regardless of the element-to-tree map and (b) each process that holds fine mesh elements has access to the meta data of all relevant trees. As an additional feature, the algorithm partitions the meta data of relevant ghost (halo) trees as well. We develop in detail how each process computes the communication pattern for the partition routine without handshaking and with minimal data movement. We demonstrate the scalability of this approach on up to 917e3 MPI ranks and .37e12 coarse mesh elements, measuring run times of one second or less.

Adaptive grid implementation for parallel continuum mechanics methods in particle simulations

“…Different SFCs are used for cell ordering, e.g. (i) Morton-curve [94] (despite being discontinuous, at most two disjoint partitions are created [95]), (ii) Hilbert curve [96], (iii) Peano curve [97], or (iv) Sierpiński curve [98]. More detailed information about SFCs can be found in [99].…”

An efficient Adaptive Mesh Refinement (AMR) algorithm for the Discontinuous Galerkin method: Applications for the computation of compressible two-phase flows

“…Introducing this flow field into Equations (1) we obtain analytical expressions for the source term w d . This source term balances viscous forces and sustains the steady state manufactured solution (32). Due to the spatial and temporal discretisation errors, this solution is distorted.…”

“…For the flow field described by (32), Equations (1) were integrated up to t tot = 0.1L/c on a computational domain of size L. Various discretisations were tested. The Reynolds number of the flow for all cases was Re = ρcL µ = 1000.…”

“…This method of cell-splitting in AMR requires a versatile data structure. According to [32], approaches to cell splitting in AMR can be classified into three distinct categories: block structured AMR (SAMR), unstructured AMR (UAMR) and tree AMR (TAMR). SAMR utilises the regular mapping of the structured grids at the expense of numerical complexity.…”

“…UAMR, on the other hand, offers the flexibility of unstructured meshes through the use of an adjacency graph. The TAMR approach, introduced in [33] and [34,32,13] for the 4est code, uses a forest of trees structure for the description of the locally refined mesh and thus creates an internal mapping [32] for the derivation of the connectivity relations of the refined grid. In the category of unstructured split cell FEM solvers, the deal-II FEM library offers an object oriented data structure [35] for AMR on hexahedral elements, and has been widely used for the solution of the Navier-Stokes equations [36].…”