Using fuzzy controllers as adaptive procedures in the finite element method

摘要

A general framework is developed to control simulation parameters that appear in finite element models in order to improve accuracy and efficiency. This approach is based on fuzzy logic that allows the expert knowledge to be taken into account on the controller design and avoids the requirement of defining a transfer function. A new feedback fuzzy controller (FC) is developed to tune the cores of the fuzzy set, producing an adaptive fuzzy controller (AFC). The designed AFC is applied to control the choice of the preconditioner to be used in an iterative solver. Its learning capability yielded a flexible controller, that can adaptively adjust the control parameters with the system changes. This methodology is also combined with a FC to drive the selection of the time step size. Numerical experiments are performed to demonstrate the performance of this novel feedback FC and its adaptive structure.