Applicability of Load Balancing Strategies to Data-Parallel Embedded Runge-Kutta Integrators
نویسندگان
چکیده
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 aim is to find out whether the employment of load balancing strategies can be profitable in spite of the additional overhead they involve.
منابع مشابه
Racoon: A parallel mesh-adaptive framework for hyperbolic conservation laws
We report on the development of a computational framework for the parallel, mesh-adaptive solution of systems of hyperbolic conservation laws like the timedependent Euler equations in compressible gas dynamics or Magneto-Hydrodynamics (MHD) and similar models in plasma physics. Local mesh refinement is realized by the recursive bisection of grid blocks along each spatial dimension, implemented ...
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 کاملParallel Execution of Embedded Runge-Kutta Methods
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 pr...
متن کاملParareal Algorithm Implementation and Simulation in Julia
We present a full implementation of the parareal algorithm—an integration technique to solve di erential equations in parallel— in the Julia programming language for a fully general, rst-order, initial-value problem. Our implementation accepts both coarse and ne integrators as functional arguments. We use Euler’s method and another Runge-Kutta integration technique as the integrators in our exp...
متن کامل