Enriched reproducing kernel particle method for fractional advection–diffusion equation
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The reproducing kernel particle method (RKPM) has been efficiently applied to problems with large deformations, high gradients and high modal density. In this paper, it is extended to solve a nonlocal problem modeled by a fractional advection–diffusion equation (FADE), which exhibits a boundary layer with low regularity. We formulate this method on a moving least-square approach. Via the enrichment of fractional-order power functions to the traditional integer-order basis for RKPM, leading terms of the solution to the FADE can be exactly reproduced, which guarantees a good approximation to the boundary layer. Numerical tests are performed to verify the proposed approach.
KeywordsMeshfree method Fractional calulus Enriched reproducing kernel Advection–diffusion equation Fractional-order basis
The project was supported partly by the National Natural Science Foundation of China (Grant 11521202). Ying is grateful for the support from the Chinese Scholarship Council. Lian and Liu are partially support by an Army Research Office (Grant W911NF-15-1-0569).