An Unstructured Semantic Mesh Definition Suitable for Finite Element Method

Marek Gayer, Hannu Niemistö and Tommi Karhelawww.marekgayer.com , www.simantics.orgTechnical Research Centre of Finland (VTT), EspooThe 14th IEEE International Conference on Computational Science and Engineering (CSE-2011), Dalian, China, August 24-26, 2011

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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

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Mesh groups (on nodes and elements)

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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)

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.

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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.

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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)

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Our Semantic mesh datastructure definition

Key Features: Abstract data features

notation Groups Property assignments

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An example model of our Semantic mesh

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Implementation of our Semantic mesh definition

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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

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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

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