Component Reuse in Iterative Solvers for the Solution of Fuzzy Partial Differential Equations

We consider elliptic partial differential equations with an uncertain diffusion parameter, where the uncertainty is modeled by fuzzy numbers or a fuzzy field. Our aim is to efficiently compute the fuzzy characteristics of the solution to the fuzzy equation. Using the so‐called α‐cut approach, it is possible to reformulate the fuzzy problem as a long sequence of global optimisation problems. Function and gradient evaluations within these optimisation problems, differ from each other through a possibly small change in one or more of the partial differential equation parameters. In order to reduce the computational complexity of the optimisation problems we consider component reuse in iterative solvers. We concentrate in particular on the reuse of the setup phase in an algebraic multigrid strategy and on reuse of initial approximations.