Theory of Functional Connections Subject to Shear-Type and Mixed Derivatives

Daniele Mortari ()
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Daniele Mortari: Aerospace Engineering, Texas A&M University, 3141 TAMU, College Station, TX 77843, USA

Mathematics, 2022, vol. 10, issue 24, 1-16

Abstract: This study extends the functional interpolation framework, introduced by the Theory of Functional Connections, initially introduced for functions, derivatives, integrals, components, and any linear combination of them, to constraints made of shear-type and/or mixed derivatives. The main motivation comes from differential equations, often appearing in fluid dynamics and structures/materials problems that are subject to shear-type and/or mixed boundary derivatives constraints. This is performed by replacing these boundary constraints with equivalent constraints, obtained using indefinite integrals. In addition, this study also shows how to validate the constraints’ consistency when the problem involves the unknown constants of integrations generated by indefinite integrations.

Keywords: functional interpolation; differential equations; numerical methods (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (1)

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