A reduced basis method for fractional diffusion operators II

Abstract We present a novel numerical scheme to approximate the solution map s ? u ( ) := ???? – f fractional PDEs involving elliptic operators. Reinterpreting as an interpolation operator allows us write integral including solutions parametrized family of local PDEs. propose reduced basis strategy on top finite element method its integrand. Unlike prior works, we deduce choice snapshots for procedure analytically. The is interpreted in spectral setting evaluate surrogate directly. Its computation boils down matrix approximation L whose inverse projected -independent space, where explicit diagonalization feasible. Exponential convergence rates are proven rigorously. A second algorithm presented avoid inversion . Instead, directly project subspace, negative power evaluated. comparison with predecessor highlights competitive performance.