Algebraic structures underneath geometric approaches

• Jari Kangas ^[1] ; Saku Suuriniemi ^[1] ; Lauri Kettunen ^[1]
  1. [1] Tampere University of Technology

     Tampere University of Technology

     Tampere, Finlandia

     
• Localización: Compel: International journal for computation and mathematics in electrical and electronic engineering, ISSN 0332-1649, Vol. 30, Nº 6 (Special Issue: Advances in Computational Electromagnetics), 2011, págs. 1715-1726
• Idioma: inglés
• Enlaces
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• Resumen

  • Purpose – The purpose of this paper is to study algebraic structures that underlie the geometric approaches. The structures and their properties are analyzed to address how to systematically pose a class of boundary value problems in a pair of interlocked complexes.

    Design/methodology/approach – The work utilizes concepts of algebraic topology to have a solid framework for the analysis. The algebraic structures constitute a set of requirements and guidelines that are adhered to in the analysis.

    Findings – A precise notion of “relative dual complex”, and certain necessary requirements for discrete Hodge‐operators are found.

    Practical implications – The paper includes a set of prerequisites, especially for discrete Hodge‐operators. The prerequisites aid, for example, in verifying new computational methods and algorithms.

    Originality/value – The paper gives an overall view of the algebraic structures and their role in the geometric approaches. The paper establishes a set of prerequisites that are inherent in the geometric approaches.