Hybrid parallelization of an adaptive finite element code

summary:We present a hybrid OpenMP/MPI parallelization of the finite element method that is suitable to make use of modern high performance computers. These are usually built from a large bulk of multi-core systems connected by a fast network. Our parallelization method is based firstly on domain decomposition to divide the large problem into small chunks. Each of them is then solved on a multi-core system using parallel assembling, solution and error estimation. To make domain decomposition for both, the large problem and the smaller sub-problems, sufficiently fast we make use of a hierarchical mesh structure. The partitioning is done on a coarser mesh level, resulting in a very fast method that shows good computational balancing results. Numerical experiments show that both parallelization methods achieve good scalability in computing solution of nonlinear, time dependent, higher order PDEs on large domains. The parallelization is realized in the adaptive finite element software AMDiS

Recursive Algorithms for Distributed Forests of Octrees

The forest-of-octrees approach to parallel adaptive mesh refinement and coarsening (AMR) has recently been demonstrated in the context of a number of large-scale PDE-based applications. Although linear octrees, which store only leaf octants, have an underlying tree structure by definition, it is not often exploited in previously published mesh-related algorithms. This is because the branches are not explicitly stored, and because the topological relationships in meshes, such as the adjacency between cells, introduce dependencies that do not respect the octree hierarchy. In this work we combine hierarchical and topological relationships between octree branches to design efficient recursive algorithms. We present three important algorithms with recursive implementations. The first is a parallel search for leaves matching any of a set of multiple search criteria. The second is a ghost layer construction algorithm that handles arbitrarily refined octrees that are not covered by previous algorithms, which require a 2:1 condition between neighboring leaves. The third is a universal mesh topology iterator. This iterator visits every cell in a domain partition, as well as every interface (face, edge and corner) between these cells. The iterator calculates the local topological information for every interface that it visits, taking into account the nonconforming interfaces that increase the complexity of describing the local topology. To demonstrate the utility of the topology iterator, we use it to compute the numbering and encoding of higher-order $C^0$ nodal basis functions. We analyze the complexity of the new recursive algorithms theoretically, and assess their performance, both in terms of single-processor efficiency and in terms of parallel scalability, demonstrating good weak and strong scaling up to 458k cores of the JUQUEEN supercomputer.Comment: 35 pages, 15 figures, 3 table

Immersogeometric analysis of compressible flows

This dissertation presents the development of a novel immersogeometric method for the simulation of turbulent compressible flows around complex geometries. The immersogeometric analysis is first extended into the version of tetrahedral finite cell method, in order to handle complex geometries flexibly and accurately. The developed method immerses complex objects into non-boundary-fitted meshes of tetrahedral finite elements which can be easily refined in interesting regions. Adaptively-refined quadrature rules faithfully capture the flow do- main geometry in the discrete problem without modifying the non-boundary-fitted finite element mesh. Particular emphasis is placed on studying the importance of the geometry resolution in in- tersected elements. Aligning with the immersogeometric concept, the results show that the faithful representation of the geometry in intersected elements is critical for accurate flow analysis. To simulate the compressible flows in an accurate and and robust way, a novel stabilized finite element formulation is developed. New weak imposition of essential boundary conditions and sliding-interface formulations are also proposed in the context of moving-domain compressible flows. The new formulation is successfully tested on a set of examples spanning a wide range of Reynolds and Mach numbers showing its superior robustness. Experimental validation of the new formulation is also carried out with good success. The developments of tetrahedral finite cell method and the stabilized finite element formulations are combined to further develop the immersogeometric method for compressible flows. Non-symmetric Nitsche method is used in the weak-boundary-condition operator, to offer good performance in the context of non-boundary-fitted discretization. The developed immersogeomet- ric method is tested against several benchmark problems, to prove its comparable accuracy to its boundary-fitted counterpart. Finally, the aerodynamic analysis of a UH-60 helicopter is carried outusing the developed method, to illustrate its potential to support design of real engineering systems through high-fidelity aerodynamic analysis