Resumen de Algebraic structures underneath geometric approaches

Jari Kangas, Saku Suuriniemi, Lauri Kettunen

• 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.