Affine approximation of parametrized kernels and model order reduction for nonlocal and fractional Laplace models

Understand

We consider parametrized problems driven by spatially nonlocal integral operators with parameter-dependent kernels.

• In particular, kernels with varying nonlocal interaction radius $\delta > 0$ and fractional Laplace kernels, parametrized by the fractional power $s\in(0,1)$, are studied.
• In order to provide an efficient and reliable approximation of the solution for different values of the parameters, we develop the reduced basis method as a parametric model order reduction approach.
• Major difficulties arise since the kernels are not affine in the parameters, singular, and discontinuous.