Dune-CurvilinearGrid: Parallel Dune Grid Manager for Unstructured Tetrahedral Curvilinear Meshes

Abstract

We introduce the dune-curvilineargrid module. The module provides the self-contained, parallel grid manager dune-curvilineargrid, as well as the underlying elementary curvilinear geometry module dune-curvilineargeometry. Both modules are developed as extension of the DUNE [3] project, and conform to the generic dune-grid and dune-geometry interfaces respectively. We expect the reader to be at least briefly familiar with the DUNE interface to fully benefit from this paper. dune-curvilineargrid is a part of the computational framework developed within the doctoral thesis of Aleksejs Fomins. The work is fully funded by and carried out at the technology company LSPR AG. It is motivated by the need for reliable and scalable electromagnetic design of nanooptical devices, achieved by HADES3D family of electromagnetic codes. It is of primary scientific and industrial interest to model full 3D geometric designs as close to the real fabricated structures as possible. Curvilinear geometries improve both the accuracy of modeling smooth material boundaries, and the convergence rate of PDE solutions with increasing basis function order [9], reducing the necessary computational effort. Additionally, higher order methods decrease the memory footprint of PDE solvers at the expense of higher operational intensity, which helps in extracting optimal performance from processing power dominated high performance architectures [30]. dune-curvilineargeometry is capable of modeling simplex entities (edges, triangles and tetrahedra) up to polynomial order 5 via hard-coded Lagrange polynomials, and arbitrary order via analytical procedures. Its most notable features are local-to-global and global-to-local coordinate mappings, symbolic and recursive integration, symbolic polynomial scalars, vectors and matrices (e.g. Jacobians and Integration Elements). dune-curvilineargrid uses the dune-curvilineargeometry module to provide the following functionality: fully parallel input of curvilinear meshes in the gmsh [10] mesh format, processing only the corresponding part of the mesh on each available core; mesh partitioning at the reading stage (using ParMETIS [16,21]); unique global indices for all mesh entities over all processes; Ghost elements associated with the interprocessor boundaries; interprocessor communication of data for shared entities of all codimensions via the standard DUNE data handle interface. There is also significant support for Boundary Integral (BI) codes, allowing for arbitrary number of interior boundary surfaces, as well as all-to-all dense parallel communication procedures. The dune-curvilineargrid grid manager is continuously developed and improved, and so is this documentation. For the most recent version of the documentation, as well as the source code, please refer to the following repositories

The DUNE Framework: Basic Concepts and Recent Developments

“…CurvilinearGrid (dune-curvilineargrid) Provides a parallel simplicial grid [21] supporting curvilinear grids read from Gmsh [22] input.…”