A multivector data structure for differential forms and equations

Jeffrey A. Chard and Vadim Shapiro

Mathematics and Computers in Simulation (MATCOM), 2000, vol. 54, issue 1, 33-64

Abstract: We use tools from algebraic topology to show that a class of structural differential equations may be represented combinatorially, and thus, by a computer data structure. In particular, every differential k-form may be represented by a formal k-cochain over a cellular structure that we call a starplex, and exterior differentiation is equivalent to the coboundary operation on the corresponding k-cochain. Furthermore, there is a one-to-one correspondence between this model and the classical finite cellular model supported by the Generalized Stokes’ Theorem and translation between the two models can be completely automated.

Keywords: Multivector data structure; Combinatorial topology; Differential equations; k-cochain (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (1)

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