Curvilinear Grid

We present Curvilinear Grid, a parallel curvilinear grid manager designed for modelling 3D PDE on large curvilinear unstructured grids. Curvilinear Grid is based on Dune library, and, besides the Dune pre-requisites, also uses ParMetis library.

Curvilinear Grid is and will remain open-source. CurvilinearGrid is owned, developed and maintained by LSPR AG, namely, its original developers. Curvilinear Grid is free for non-commercial use. Commercial use is negotiable. Commercial use also to be negotiated with owners of pre-requisite libraries (e.g. ParMetis). Curvilinear Grid is an ongoing project. We warmly welcome contributions for the community.

News

12.12.2016 - First version of Curvilinear Grid documentation submitted to Arxiv

29.09.2015 - First stable version of Curvilinear Grid is presented at Dune user meeting

Current Features

Below presented is a brief list of most important features of Curvilinear Grid and Curvilinear Geometry.

Curvilinear Geometry

• Numeric Lagrange Interpolation of simplex geometries dimension 1 to 3 orders 1 to 5
• Analytic Lagrange Interpolation of simplex geometries of arbitrary order
• Analytic polynomials of arbitrary dimension and order. Includes arithmetic, partial derivatives, exact integrals over reference element, caching
• Local-to-global mapping for simplex elements via Lagrange Polynomials
• Global-to-local mapping via Newton method
• Analytic differential quantities: jacobians, integration elements, surface normals
• Recursive integration for non-polynomial integrands. Based on quadrature rules provided by dune-geometry
• Recursive integration of vector and matrix quantities for efficiency
• Geometry caching

Curvilinear GMSH Reader

• Reads .msh meshes produced by GMSH
• Reads curvilinear meshes order 1-5
• Scalable reading of large parallel meshes with no memory bottleneck
• Automatic mesh partitioning via ParMetis
• Provides GridFactory with all vertices, elements and boundary segments.
• Provides GlobalIndex for vertices, elements and boundary segments, reused from .msh file
• Provides Tag for all elements and boundary segments. The tag is used by GMSH to distinguish between elements and faces of different type (e.g. material properties, subdomains, interior surfaces)

Curvilinear VTK Writer

• Writes Grids or individual elements in parallel to VTK, VTU and PVTU files. Such files can be visualised by, e.g. ParaView or VisIt
• Can write entities of any codimension separately
• For each entity additional scalar data is provided for better visualisation: partition type, containing process rank and tag
• Flexible virtual refinement for visualisation of curvature
• Arbitrary number of user-defined vector fields can be added to the same grid
• Mesh explosion option to better visualise individual elements

Curvilinear Grid

• Self-contained parallel grid manager
• Entities provide curvature order and physical tag
• GlobalIndex for entities of all codimensions
• Ghost elements
• Grid diagnostics: VTK, element self-intersection test, statistics on element quality (in future, also mesh balance)
• LoggingMessage for runtime text output with flexible parallel output and compile-time controllable verbosity
• LoggingTimer for parallel timing of parts of code. Sums up multiple uses of same code. Reports parallel statistics
• Communication via DataHandle for all codimensions and all protocols prescribed by DataHandle interface
• Wrapper for MPI-3 Neighbor All-to-all communication methods

Nearest Future

We are currently working on the following features, which should see light within the coming months

• Utility for calculating singular integrals - useful, for examile, in Surface Integral Methods
• Improvement of curvilinear geometry interpolation for p-convergence

Documentation

The documentation as of 12.12.2016 is available on Arxiv. The documentation source code is located in the /doc/manual/ folder of the Curvilinear Grid Module. We regularly update this documentation. This section will contain the most recent PDF version of the documentation when the Arxiv one is no longer representative. We are aware that the documentation is currently incomplete, so we recommend the user to read the source code or contact us in case of further questions. The comments given directly in the source code will provide additional support.

Examples

Curvilinear VTK Writer naturally outputs grid entities of different structural type. Below images demonstrate total mesh, as well as interior elements, domain boundaries, processor boundaries and ghost elements in the corresponding order. Note that ParaView does not naturally support output of curvilinear entities, so a virtual refinement is used to visualise smooth surfaces. Hence the elements appear to consist of linear triangles, while the are actually smooth


Curvilinear GMSH Reader is able to read meshes completely in parallel, without having to funnel the initial data file through the master process. To demonstrate that, we present a BullsEye geometry mesh of 4.4 million elements, read by Curvilinear GMSH Reader on 12 cores and written to VTK by Curvilinear VTK Writer. The first image presents the disk only, colored by the containing processor. Note that the mesh also contains an air bubble around the disk, which is disabled directly in ParaView by subselecting only the element tags of the disk itself. The 2nd image presents the ghost elements of the entire mesh, colored by the element tag (metal is red, air is white and boundary layer is light blue).


The below example is a mesh of a cylindric plasmonic cavity with curved edges, studied in the PhD thesis of Aleksejs Fomins. The first image is a vertical cut through the center of the mesh, colored by the material tag of the element. The second is a subset of the mesh, corresponding to the material tag of the dispersive dielectric layer.


We would also like to present some videos of electromagnetic simulations over curvilinear grids, performed by our full 3D DG Frequency Domain solver Hades3d.

• Herzian dipole, radiating into free space
• Mie scattering of plane waves by a gold nanosphere in vacuum

Download

Currently the Curvilinear Grid is available in the trunk version. Note that the Curvilinear Grid requires Curvilinear Geometry. Please use

git clone https://github.com/LSPR-AG/dune-curvilineargeometry.git
git clone https://github.com/LSPR-AG/dune-curvilineargrid.git

to clone both modules into the folder already containing the core dune modules. Click here for detailed installation instructions.

Contribute

Since Curvilinear Grid is open-source, we are open to contributions from the community. We are also interested in supervising Masters Thesis and summer projects for students interested in numerical methods and their application to modeling. Please contact us for more details.

Contact us

Curvilinear Grid is developed by LSPR AG
Grubenstrasse 9,
CH-8045 Zürich,
Switzerland
Email: curvilineargrid at lspr dot ch
Phone: +41 43 366 90 74
Follow @curvgrid

The original authors of Curvilinear Grid are
Aleksejs Fomins (aleksejs dot fomins at lspr dot ch)
Benedikt Oswald (benedikt dot oswald at lspr dot ch)

Do not hesitate to contact us with enquiries, suggestions, proposals, bug reports, etc

Last Update: 12 Dec 2016