INTEGRATING GEOMETRIC ALGEBRA AND DIFFERENTIAL FORMS: HISTORICAL EVOLUTION, MATHEMATICAL FOUNDATIONS, AND CORE EQUATIONS
DOI:
https://doi.org/10.29121/shodhkosh.v2.i2.2021.4482Keywords:
Geometric Algebra, Differential Formsp, Multivectors, Exterior Derivative, Wedge Product, Computational Geometry, Multidimensional AnalysisAbstract [English]
Geometric Algebra and Differential Forms are two mathematical tools, which have different historical roots but illuminate similar aspects of the multi-dimensional settings. Various mathematical theories and their historical evolution, as well as attempts to integrate them, are discussed in this paper. From such developments, the work develops a integrating paradigm using commonalities for reducing computational complexity for matters such as electromagnetism, fluid dynamics, and geometry computation. This paper explores the fundamental concepts of both frameworks, highlighting their similarities, differences, and potential synergies. The results show that there is a great potential for integration of these frameworks in order to solve multi-faceted issues. The conclusion of the paper addresses issues of trend, future challenges and research directions.
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