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SUMMARYA 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.

In this work, a stable Petrov–Galerkin formulation is combined with an hp‐adaptive refinement strategy. The stability engendered by this formulation allows the use of high interpolation element order in regions with steep gradients. The new hp‐adaptive strategy, originally proposed for elliptic problems, simultaneously computes the new mesh parameters (element length and element interpolation order) and works fine for hyperbolic problems, yielding promising computational savings. Copyright © 2002 John Wiley & Sons, Ltd.

SUMMARYThe solution of the Crank-Nicolson (CN) method may present spurious modes, which mostly happens in systems with an initial singularity. In this work, we analyze the onset of spurious oscillations for the CN method for large time steps. This analysis is performed on the general one-dimensional linear advection-diffusion-reaction transport equation with initial singularity that models a broad range of mass transfer phenomena in natural and engineering sciences. The discrete problem is obtained using a stable finite element method in space and the generalized trapezoidal family of methods in time. Depending on the range of parameters, either the Galerkin or the streamline upwind Petrov-Galerkin methods are used to guarantee stability in space. We derive a stability analysis of the fully discrete method and investigate the techniques proposed in the literature to damp oscillations. We propose a new threshold of time oscillations to overcome the spurious modes, which is also extended to deal with nonlinear problems.

SUMMARYIt is well known that Krylov-Schwarz methods are well suited for solving linear systems of equations in high-latency, distributed memory environments and constitute powerful tools when combined with Newton-Krylov methods to solve Computational Fluid Dynamics problems. Nevertheless, the computational costs related to the Jacobian and the preconditioner evaluation can sometimes be prohibitive. In this work a strategy to reduce these costs is presented, based on evaluating a new preconditioner only after it had been frozen for several time steps. Numerical experiments show the computational gain achieved with the proposed strategy.