Decoupling method for parallel Delaunay two-dimensional mesh generation

Parallel mesh generation procedures that are based on geometric domain decompositions require the permanent separators to be of good quality (in terms of their angles and length), in order to maintain the mesh quality. The Medial Axis Domain Decomposition, an innovative geometric domain decomposition procedure that addresses this problem, is introduced. The Medial Axis domain decomposition is of high quality in terms of the formed angles, and provides separators of small size, and also good work-load balance. It presents for the first time a decomposition method suitable for parallel meshing procedures that are based on geometric domain decompositions.;The Decoupling Method for parallel Delaunay 2D mesh generation is a highly efficient and effective parallel procedure, able to generate billions of elements in a few hundred of seconds, on distributed memory machines. Our mathematical formulation introduces the notion of the decoupling path, which guarantees the decoupling property, and also the quality and conformity of the Delaunay submeshes. The subdomains are meshed independently, and as a result, the method eliminates the communication and the synchronization during the parallel meshing. A method for shielding small angles is introduced, so that the decoupled parallel Delaunay algorithm can be applied on domains with small angles. Moreover, I present the construction of a sizing function, that encompasses an existing sizing function and also geometric features and small angles. The decoupling procedure can be used for parallel graded Delaunay mesh generation, controlled by the sizing function

Programming Abstractions for Data Locality

The goal of the workshop and this report is to identify common themes and standardize concepts for locality-preserving abstractions for exascale programming models. Current software tools are built on the premise that computing is the most expensive component, we are rapidly moving to an era that computing is cheap and massively parallel while data movement dominates energy and performance costs. In order to respond to exascale systems (the next generation of high performance computing systems), the scientific computing community needs to refactor their applications to align with the emerging data-centric paradigm. Our applications must be evolved to express information about data locality. Unfortunately current programming environments offer few ways to do so. They ignore the incurred cost of communication and simply rely on the hardware cache coherency to virtualize data movement. With the increasing importance of task-level parallelism on future systems, task models have to support constructs that express data locality and affinity. At the system level, communication libraries implicitly assume all the processing elements are equidistant to each other. In order to take advantage of emerging technologies, application developers need a set of programming abstractions to describe data locality for the new computing ecosystem. The new programming paradigm should be more data centric and allow to describe how to decompose and how to layout data in the memory.Fortunately, there are many emerging concepts such as constructs for tiling, data layout, array views, task and thread affinity, and topology aware communication libraries for managing data locality. There is an opportunity to identify commonalities in strategy to enable us to combine the best of these concepts to develop a comprehensive approach to expressing and managing data locality on exascale programming systems. These programming model abstractions can expose crucial information about data locality to the compiler and runtime system to enable performance-portable code. The research question is to identify the right level of abstraction, which includes techniques that range from template libraries all the way to completely new languages to achieve this goal

Graded Delaunay Decoupling Method 2

Parallel computing has made possible large scale simulations of physical phenomena. These simulations usually employ a finite element approach and they require the creation of large meshes with good quality. The core mesh refinement procedure is fast, but memory intensive, and in order to create efficiently a large mesh we have to utilize parallel machines. We present a method for creating large 2D graded Delaunay meshes on distributed memory machines. The method decouples the mesh generation procedure on each subdomain, and thus eliminates the communication, while the final mesh is of guaranteed quality. This work extents previous results [24], by allowing the element size to be governed by a sizing function, or a background grid, and so producing large graded meshes. The Delaunay decoupling method demonstrates high efficiency, billions of elements can be created in less than 2.5 minutes, and it is effective, using well tested and fine tuned sequentia

Global tide simulations with ICON-O: testing the model performance on highly irregular meshes

The global tide is simulated with the global ocean general circulation model ICON-O using a newly developed tidal module, which computes the full tidal potential. The simulated coastal M2 amplitudes, derived by a discrete Fourier transformation of the output sea level time series, are compared with the according values derived from satellite altimetry (TPXO-8 atlas). The experiments are repeated with four uniform and sixteen irregular triangular grids. The results show that the quality of the coastal tide simulation depends primarily on the coastal resolution and that the ocean interior can be resolved up to twenty times lower without causing considerable reductions in quality. The mesh transition zones between areas of different resolutions are formed by cell bisection and subsequent local spring optimisation tolerating a triangular cell’s maximum angle up to 84°. Numerical problems with these high-grade non-equiangular cells were not encountered. The results emphasise the numerical feasibility and potential efficiency of highly irregular computational meshes used by ICON-O.Deutsche Forschungsgemeinschaft http://dx.doi.org/10.13039/50110000165