Model reduction for fractional elliptic problems using Kato's formula

<p style='text-indent:20px;'>We propose a novel numerical algorithm utilizing model reduction for computing solutions to stationary partial differential equations involving the spectral fractional Laplacian. Our approach utilizes known characterization of solution in terms an integral local (classical) elliptic problems. We reformulate this into expression whose continuous and discrete formulations are stable; stable independent all discretization parameters. subsequently apply reduced basis method accomplish order integrand. choice quadrature is global Gaussian rule that we observe more efficient than previously proposed rules. Finally, enables one compute multi-query Laplace problems with orders magnitude less cost traditional solver.</p>