Adaptive Iterative Explicit Time Integration for Nonlinear Heat Conduction Problems

Three explicit time integration schemes are compared for solving nonlinear heat conduction problems, local iteration monotone scheme, nonlinear exponential Euler scheme and a scheme based on the hyperbolic model of heat conduction, where an artificial second order time derivative term is added to stabilize the computations. The local iteration monotone and exponential Euler schemes are monotone and allow for a sufficiently large time step size. The local iteration monotone scheme is based on a special Chebyshev polynomial approximation, whereas the exponential Euler scheme employs a restarted Krylov subspace procedure. For these two schemes we propose an adaptive time step selection strategy which leads to a significant reduction in computational costs.