Embedded pairs of Fractional Step Runge-Kutta methods and improved Domain Decomposition techniques for parabolic problems

In this paper we design and apply new embedded pairs of Fractional Step Runge-Kutta methods to the efficient resolution of multidimensional parabolic problems. These time integrators are combined with a suitable splitting of the elliptic operator subordinated to a decomposition of the spatial domain and a standard spatial discretization. With this technique we obtain parallel algorithms which have the main advantages of classical Domain Decomposition methods and, besides, avoid iterative processes like Schwarz iterations, typical of them. The use of these embedded methods permits to get a fast variable step time integration process.