Abstract
In this chapter a numerical method is presented for efficient solution of many differential equations with arbitrary domains using geometrical transformation and Kronecker product rules. Initially, a mesh free formulation for rectangular domains is developed and a full decomposition of matrix equations is achieved using Kronecker product rules. The solution of a governing equation on an arbitrary domain is sought through a geometrical transformation from the rectangular domain into the original domain using conformal mapping. The efficiency of the proposed method is examined using various engineering examples.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Shojaei, I., Rahami, H., Kaveh, A.: A numerical solution for Laplace and Poisson’s equations using geometrical transformation and graph products. Appl. Math. Modell. 40(17–18), 7768–7783 (2016)
Zhang, X., Liu, X.H., Song, K.Z., Lu, M.W.: Least-squares collocation meshless method. Int. J. Numer. Methods Eng. 51, 1089–1100 (2001)
Davie, A.M., Stothers, A.J.: Improved bound for complexity of matrix multiplication. Proc. R. Soc. Edinburgh: Section A: Math. 143, 351–369 (2013)
Kaveh, A.: Optimal Analysis of Structures by Concepts of Symmetry and Regularity. Springer, GmbH, Wien-New York (2013). https://doi.org/10.1007/978-3-7091-1565-7
Kaveh, A., Shojaei, I., Rahami, H.: New developments in the optimal analysis of regular and near-regular structures: decomposition, graph products, force method. Acta Mech. 226(3), 665–681 (2015)
Kaveh, A., Rahami, H.: Tri-diagonal and penta-diagonal block matrices for efficient eigensolutions of problems in structural mechanics. Acta Mech. 192, 77–87. (2007). http://www.springerlink.com/content/p62629m74120/?p=cc0dadc6e55a410daf169b171a7aca74&pi=0
Papamichael, N., Stylianopoulos, N.: Numerical Conformal Mapping: Domain Decomposition and the Mapping of Quadrilaterals. World Scientific, New Jersey (2010)
Driscoll, T.A., Trefethen, L.N.: Schwarz-Christoffel Mapping. Cambridge University Press (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Kaveh, A., Rahami, H., Shojaei, I. (2020). Mappings for Transformation of Near-Regular Domains to Regular Domains. In: Swift Analysis of Civil Engineering Structures Using Graph Theory Methods. Studies in Systems, Decision and Control, vol 290. Springer, Cham. https://doi.org/10.1007/978-3-030-45549-1_9
Download citation
DOI: https://doi.org/10.1007/978-3-030-45549-1_9
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-45548-4
Online ISBN: 978-3-030-45549-1
eBook Packages: EngineeringEngineering (R0)