Parallel iteration of high-order Runge-Kutta methods with stepsize control
نویسنده
چکیده
This paper investigates iterated Runge-Kutta methods of high order designed in such a way that the right-hand side evaluations can be computed in parallel. Using stepsize control based on embedded formulas a highly efficient code is developed. On parallel computers, the 8th-order mode of this code is more efficient than the DOPR18 implementation of the formulas of Prince and Dormand. The lOth-order mode is about twice as cheap for comparable accuracies.
منابع مشابه
Adaptive Stepsize Control in Implicit Runge-Kutta Methods for Reservoir Simulation
This paper concerns predictive stepsize control applied to high order methods for temporal discretization in reservoir simulation. The family of Runge-Kutta methods is presented and in particular the explicit singly diagonally implicit Runge-Kutta (ESDIRK) methods are described. A predictive stepsize adjustment rule based on error estimates and convergence control of the integrated iterative so...
متن کاملDiagonal Implicitly Iterated Runge Kutta Methods on Distributed Memory Multiprocessors
We investigate the parallel implementation of the diagonal implicitly iterated Runge Kutta DIIRK method an iteration method based on a predictor corrector scheme This method is appropriate for the solution of sti systems of ordinary di erential equations ODEs and provides embedded formulae to control the stepsize We discuss di erent strate gies for the implementation of the DIIRK method on dist...
متن کاملParallel Iterated Runge Kutta Methods and Applications
The iterated Runge Kutta IRK method is an iteration scheme for the numerical solu tion of initial value problems IVP of ordinary di erential equations ODEs that is based on a predictor corrector method with an Runge Kutta RK method as corrector Embed ded approximation formulae are used to control the stepsize We present di erent parallel algorithms of the IRK method on distributed memory multip...
متن کاملControl Strategies for the Iterative Solution of Nonlinear Equations in ODE Solvers
In the numerical solution of ODEs by implicit time-stepping methods, a system of (nonlinear) equations has to be solved each step. It is common practice to use xed-point iterations or, in the stii case, some modiied Newton iteration. The convergence rate of such methods depends on the stepsize. Similarly, a stepsize change may force a refactorization of the iteration matrix in the Newton solver...
متن کاملEmbedded Diagonally Implicit Runge - Kutta Algorithms on Parallel Computers
This paper investigates diagonally implicit Runge-Kutta methods in which the implicit relations can be solved in parallel and are singly diagonalimplicit on each processor. The algorithms are based on diagonally implicit iteration of fully implicit Runge-Kutta methods of high order. The iteration scheme is chosen in such a way that the resulting algorithm is ^(a)-stable or Z,(a)-stable with a e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2001