Adaptive finite element method for fractional differential equations using hierarchical matrices.

Zhao, Xuan.

Hu, Xiaozhe.

Cai, Wei.

Karniadakis, George.


  • A robust and fast solver for the fractional differential equation (FDEs) involving the Riesz fractional derivative is developed using an adaptive finite element method. It is based on the utilization of hierarchical matrices (-Matrices) for the representation of the stiffness matrix resulting from the finite element discretization of the FDEs. We employ a geometric multigrid method for the solution ... read more
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  • Zhao, Xuan, Xiaozhe Hu, Wei Cai, and George Em Karniadakis. "Adaptive Finite Element Method for Fractional Differential Equations Using Hierarchical Matrices." Computer Methods in Applied Mechanics and Engineering 325 (October 2017): 56-76.
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