1. An Unstructured Semantic Mesh Definition Suitable for Finite Element Method Marek Gayer, Hannu Niemistö and Tommi Karhela www.marekgayer.com, www.simantics.org Technical Research Centre of Finland (VTT), Espoo The 14th IEEE International Conference on Computational Science and Engineering (CSE-2011), Dalian, China, August 24-26, 2011

2. 2 05/02/2016 Introduction - Finite Element Method and Mesh  Finding solution for Partial Differential equations for evaluation of characteristics (e.g. potential, concentrations)  Discretizes continuum (i.e. modeled object) into finite number of elements – e.g. triangles: 2D, tetrahedron: 3D  Characteristics are determined in the nodes of the element  Suitable discretization of continuous domain to simple volume cell elements  Partial differential equations (PDE’s) can be replaced by system of non-linear algebraic equations

3. 3 05/02/2016 Mesh groups (on nodes and elements)

4. 4 05/02/2016 Demystifying “semantic modelling approach” and Semantic graph  Defining semantics ~ Adding “meaning” of data objects by specifying their relations and by annotating them using statements.  Based on ontologies (basically “objects and relations between them” model, see: http://en.wikipedia.org/wiki/Ontology_(information_science) http://en.wikipedia.org/wiki/Ontology_(information_science)  Data consists of resources, statements (forming triplets) and literals.  Resource: a node of the graph. A resource has a unique identity.  Statement: an edge of the graph. A statement consists of three resources: subject, predicate (relation), object.  Literal: any binary data attached to a resource.

5. 5 05/02/2016 Example – Ontology based simulation model configuration in APROS 6 Different modelling and simulation approaches are modelled as ontologies and mapped together to form a consistent graph of model configurations.

6. 6 05/02/2016 Requirements and features of our Semantic mesh proposal  Limited number of semantic resources (due to performance and low memory consumption)  Simplicity, rich data model description even with limited number of resources  Extendibility (possible adding of eventual new features utilizing current concepts)

7. 7 05/02/2016 Our Semantic mesh datastructure definition  Key Features:  Abstract data features notation  Groups  Property assignments

8. 8 05/02/2016 An example model of our Semantic mesh

9. 9 05/02/2016 Implementation of our Semantic mesh definition

10. 10 05/02/2016

11. 11 05/02/2016 Additional future work includes:  Import from other FEM formats  Special mesh ontologies for concrete formats  Transformation of ontologies using Simantics Constraint Language  New CFD/FEM environment with special impact of 1D/3D process simulator integration

12. 12 05/02/2016 Conclusion  The Semantic mesh definition  Number of semantic components necessary to allocate in a semantic database is limited =>  Reasonable memory requirements  Can be used for even very large meshes (millions of nodes and elements  Generality and extendibility  Tested in the semantic database in Simantics software platform and in our FEM integration software application

13. 13 05/02/2016 VTT creates business from technology