Three-Dimensional Thermo-Acousto-Electric Diagonalized and Supplementary Equations in Fully Tri-Anisotropic and Inhomogeneous Media Part II: Relative Proof of Consistency

• Published in: IEEE journal on multiscale and multiphysics computational techniques Vol. 3; pp. 159 - 166
• Main Author: Baghai-Wadji, Alireza
• Format: Journal Article
• Language: English
• Published: Piscataway IEEE 2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Anisotropy; Bills of materials; Computational modeling; Consistency; Formulas (mathematics); Inhomogeneous media; Mathematical analysis; Mathematical model; Nonhomogeneous media; Operators (mathematics); Partial differential equations; piezoelectricity; SAW filters; Structural integrity; Symmetric matrices; thermoelectricity; Three-dimensional displays; Writing
• ISSN: 2379-8815; 2379-8815
• DOI: 10.1109/JMMCT.2018.2873177

The accompanying paper (PartI: Proof of Existence by Construction) in this transactions presents the diagonalization of coupled thermo-acousto-electric governing (G) and constitutive (C) systems of equations in fully tri-anisotropic and inhomogeneous media in three spatial dimensions. The construction of a set of associated supplementary partial differential equations has also been detailed in Part I. In this paper, distinct features of the diagonalized (D) and associated supplementary (S) systems of equations along with their constituent block operator matrices are scrutinized. It is rigorously shown that the constructed (D, S) equations are internally consistent and sharply equivalent with the originating (G, C) equations. Apart from firmly establishing the structural integrity of the (D, S) equations, the provided (relative) proof of consistency illuminates the interwoven relationships between the (D, S) and (G, C) systems of equations.