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Solving large-scale problems by Taylor Meshless method

Abstract : A true integration-free meshless method based on Taylor series named Taylor meshless method (TMM) has been proposed to solve two-dimensional partial differential equations (PDEs). In this framework, the shape functions are approximated solutions of the PDE, and the discretization concerns only the boundary. In this paper, the applicability of TMM to solve large-scale problems is discussed under two aspects. First, as in some other meshless methods, ill-conditioned matrices and round-off error propagation could lead to a loss of accuracy when the number of unknowns increases. This point will be investigated in the case of large-scale problems. Second, the computation time and its distribution are analyzed from numerical experiments for PDEs in a 3D domain. It is established that the TMM method is efficient and robust, even in the case of large-scale problems, while the finite element numerical model involves more than 3 million degrees of freedom.
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https://hal.univ-lorraine.fr/hal-03251215
Contributor : Farid Abed-Meraim <>
Submitted on : Sunday, June 6, 2021 - 6:31:28 PM
Last modification on : Tuesday, June 8, 2021 - 3:55:55 PM

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Jie Yang, Heng Hu, Michel Potier-Ferry. Solving large-scale problems by Taylor Meshless method. International Journal for Numerical Methods in Engineering, Wiley, 2017, 112 (2), pp.103-124. ⟨10.1002/nme.5508⟩. ⟨hal-03251215⟩

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