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K-DIMENSIONAL MATRICES IN NUMERICAL SOLUTION OF DIFFUSION PROBLEMS

DOI: 10.1615/ICHMT.2017.CHT-7.1300
pages 1203-1206

Oronzio Manca
Dipartimento di Ingegneria Industriale e dell'Informazione, Università degli Studi della Campania "Luigi Vanvitelli," Aversa (CE), Italy

Raimondo Manca
Dipartimento di Metodi e Modelli per il Territorio, L'Economia e La Finanza, Università "La Sapienza", Via del Castro Laurenziano 9, I−00161 Roma, Italy

Аннотация

A generalization to N-dimensions of the tridiagonal matrix algorithm is proposed employing K-dimensional matrices. The correspondence between the spatial dimension of the problem and the dimension of this kind of matrix structure is shown. The proposed method allows to solve multidimensional problems for partial differential equations with a number of variables N greater than 4. The proposed approach extends the Thomas algorithm to any dimensions in the sense that the tridiagonal concept is generalized to a tridiagonal structured matrix where each of the matrix can be a matrix.

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