Parameter optimization and benchmark verification of a local radial basis function collocation method for transient heat conduction in multilayer thin-walled structures

Tao Ding; Yuanjian Lin; Tao Ding; Yuanjian Lin

doi:10.3934/math.20261064

AIMS Mathematics

2026, Volume 11, Issue 8: 26538-26567. doi: 10.3934/math.20261064

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Research article

Parameter optimization and benchmark verification of a local radial basis function collocation method for transient heat conduction in multilayer thin-walled structures

Tao Ding ^,,
Yuanjian Lin

School of Intelligent Construction, Wuxi Taihu University, Wuxi 214064, China

Received: 15 June 2026 Revised: 28 July 2026 Accepted: 07 August 2026 Published: 25 August 2026
MSC : 65M70, 65M12, 80M22

This paper calibrates and verifies a local radial basis function collocation method (LRBFCM) for transient heat conduction in multilayer thin-walled structures. The discrete system is stated in full, including the row construction for interior, Dirichlet, Neumann, and interface nodes and the load vector required by inhomogeneous Dirichlet data. The method is verified against the exact series solution of the single-layer benchmark through error norms and spatial and temporal convergence studies, together with a steady series-resistance check of the interface treatment. A fixed-domain calibration expresses the shape parameter nondimensionally as $ c = \beta h $ and identifies the wall thickness as a candidate length scale for the tested configuration. On the tested single-layer node set, later-time accuracy and early-time undershoot are found to vary in opposite directions as the local stencil is widened, and documented finite element runs show a corresponding contrast between element orders. Multilayer simulations of two- and five-layer composite walls illustrate the calibrated scheme.
Citation: Tao Ding, Yuanjian Lin. Parameter optimization and benchmark verification of a local radial basis function collocation method for transient heat conduction in multilayer thin-walled structures[J]. AIMS Mathematics, 2026, 11(8): 26538-26567. doi: 10.3934/math.20261064

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Abstract

This paper calibrates and verifies a local radial basis function collocation method (LRBFCM) for transient heat conduction in multilayer thin-walled structures. The discrete system is stated in full, including the row construction for interior, Dirichlet, Neumann, and interface nodes and the load vector required by inhomogeneous Dirichlet data. The method is verified against the exact series solution of the single-layer benchmark through error norms and spatial and temporal convergence studies, together with a steady series-resistance check of the interface treatment. A fixed-domain calibration expresses the shape parameter nondimensionally as $ c = \beta h $ and identifies the wall thickness as a candidate length scale for the tested configuration. On the tested single-layer node set, later-time accuracy and early-time undershoot are found to vary in opposite directions as the local stencil is widened, and documented finite element runs show a corresponding contrast between element orders. Multilayer simulations of two- and five-layer composite walls illustrate the calibrated scheme.

References

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