Parallel Execution of Embedded Runge-Kutta Methods
نویسندگان
چکیده
In this paper, we consider the parallel solution of nonstii ordinary diierential equations with two diierent classes of Runge-Kutta (RK) methods providing embedded solutions: classical embedded RK methods and iterated RK methods which were constructed especially for parallel execution. For embedded Runge-Kutta methods, mainly the potential system parallelism is exploited. Iterated RK methods provide an additional source of parallelism in the form of independent function evaluations, but they usually require a higher number of function evaluations.
منابع مشابه
Embedded 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 کاملParallel iteration of high-order Runge-Kutta methods with stepsize control
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-o...
متن کاملApplicability of Load Balancing Strategies to Data-Parallel Embedded Runge-Kutta Integrators
Embedded Runge-Kutta methods are among the most popular methods for the solution of non-stiff initial value problems of ordinary differential equations (ODEs). We investigate the use of load balancing strategies in a dataparallel implementation of embedded Runge-Kutta integrators. Since the parallelism contained in the function evaluation of the ODE system is typically very fine-grained, our ai...
متن کاملEmbedded 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 h...
متن کاملEffiziente Implementierung eingebetteter Runge-Kutta-Verfahren durch Ausnutzung der Speicherzugriffslokalität
Embedded Runge-Kutta methods are among themost popular numerical solutionmethods for non-stiff initial value problems of ordinary differential equations. While possessing a simple computational structure, they provide desirable numerical properties and can adapt the step size efficiently. Therefore, embedded Runge-Kutta methods can often compute the solution function faster than other solution ...
متن کامل