Mapping techniques for collocation method of time-fractional convection–diffusion equations in domains with cracks

Bongsoo Jang and Hyunju Kim

Mathematics and Computers in Simulation (MATCOM), 2024, vol. 217, issue C, 60-79

Abstract: This paper proposes numerical methods that effectively deal with time-fractional convection–diffusion equations containing crack singularities. To deal with singularities, we design the geometrical mapping whose push-forward from the parameter space into the physical space generates point singularity functions based on the parametrization of the circular arc and NURBS (non-uniform rational B-spline). We adopt the collocation method with B-spline basis functions to approximate the solution in the spatial direction and enrich the approximation space by k-refinements in IGA (Isogeometric Analysis). For the discretization along the temporal direction, we employ the explicit Predictor-Corrector (PC) scheme that has the order 2−ν and 3−ν of the truncation error for the linear and quadratic interpolation, respectively. Taking advantage of the NURBS geometrical mapping, we demonstrate the performance of the proposed methods applying to time-fractional convection–diffusion equations with nonlinear terms on curved domains containing crack singularities.

Keywords: Mapping method; Isogeometric collocation method; Time fractional convection–diffusion equations; Crack or corner singularities; Caputo fractional derivative; Predictor-corrector scheme (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:217:y:2024:i:c:p:60-79

DOI: 10.1016/j.matcom.2023.10.014

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