Simulation is used in many branches of industry to understand the physical behaviour and properties of products designed by CAD-systems. The simulation results are in many cases scalar or vector fields, related to the inside of the object or the space around the object. The expected introduction of iso-geometric representation and analysis will join together CAD and FEM descriptions of geometry, and simplify the use of higher order elements in simulation systems. Consequently result-describing fields will frequently be ones with a higher order description than used today. Such higher order field descriptions allow for more singularities and intricate behaviour than the current lower order descriptions, so understanding and classifying the fields will be a challenge.

The project will address fields represented by piecewise polynomials, and regard such fields as piecewise algebraic surfaces. Thus knowledge from real algebraic geometry can help to interpret and classify the fields to ensure proper understanding of field properties, singularities and their visualization.

The project will also consider the possibility of converting large triangulations or structures of CAD-surfaces to a piecewise algebraic representation by extending approximate implicitization to piecewise algebraic surfaces.

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