A fast method for a generalized nonlocal elastic model

We develop a numerical method for a generalized nonlocal elastic model, which is expressed as a composition of a Riesz potential operator with a fractional differential operator, by composing a collocation method with a finite difference discretization.By carefully exploring the structure of the coefficient matrix of the numerical method, we develop a preconditioned fast Krylov subspace method, which reduces the computations to ( N log ? N ) per iteration and the memory to O ( N ) . The use of the preconditioner significantly reduces the number of iterations, and the preconditioner can be inverted in O ( N log ? N ) computations. Numerical results show the utility of the method.

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