Load balancing schemes for extrapolation methods

Rauber, Thomas; Rünger, Gudula

doi:10.1002/(sici)1096-9128(199703)9:3<181::aid-cpe245>3.0.co;2-6

Cited by 23 publications

(11 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Depending on the problem type and its stiffness, however, traditional RK or LM schemes require nonlinear solver iterations, whereas extrapolated IMEX schemes may not; they are similar to W-methods but can achieve much higher orders of convergence. Moreover, the extrapolation methods can be easily parallelized [26] as each entry on T j,1 can be computed independently. Furthermore, the computational cost is predetermined: cost for T jk ∝ j(j + 1)/2 function evaluations, and thus each entry can be optimally scheduled on multiprocessor or multicore architectures.…”

Section: Split-imex Methodmentioning

confidence: 99%

Extrapolated Implicit-Explicit Time Stepping

Constantinescu¹,

Sandu²

2010

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

This paper constructs extrapolated implicit-explicit time stepping methods that allow one to efficiently solve problems with both stiff and nonstiff components. The proposed methods are based on Euler steps and can provide very high order discretizations of ODEs, index-1 DAEs, and PDEs in the method-of-lines framework. Implicit-explicit schemes based on extrapolation are simple to construct, easy to implement, and straightforward to parallelize. This work establishes the existence of perturbed asymptotic expansions of global errors, explains the convergence orders of these methods, and studies their linear stability properties. Numerical results with stiff ODE, DAE, and PDE test problems confirm the theoretical findings and illustrate the potential of these methods to solve multiphysics multiscale problems.

show abstract

Section: Split-imex Methodmentioning

confidence: 99%

Extrapolated Implicit-Explicit Time Stepping

Constantinescu¹,

Sandu²

2010

SIAM J. Sci. Comput.

View full text Add to dashboard Cite

show abstract

“…Extrapolation methods Extrapolation methods are explicit solution methods for ODEs with a possibly high convergence order [9,17]. They are widely used and are especially suited if high precision is required.…”

Section: Runtime Experimentsmentioning

confidence: 99%

Library Support for Hierarchical Multi-Processor Tasks

Rauber

Rünger²

2002

ACM/IEEE SC 2002 Conference (SC'02)

View full text Add to dashboard Cite

The paper considers the modular programming with hierarchically structured multi-processor tasks on top of SPMD tasks for distributed memory machines. The parallel execution requires a corresponding decomposition of the set of processors into a hierarchical group structure onto which the tasks are mapped. This results in a multi-level group SPMD computation model with varying processor group structures. The advantage of this kind of mixed task and data parallelism is a potential to reduce the communication overhead and to increase scalability. We present a runtime library to support the coordination of hierarchically structured multi-processor tasks. The library exploits an extended parallel group SPMD programming model and manages the entire task execution including the dynamic hierarchy of processor groups. The library is built on top of MPI, has an easy-to-use interface, and leads to only a marginal overhead while allowing static planning and dynamic restructuring.

show abstract

“…Because the computations for the different stepsizes are independent of each other, parallelism across the method can be exploited [6,18]. An efficient solution method for parallel machines with large numbers of processors can be obtained by using several processors for each stepsize among which the ODE system is distributed, i.e., by additionally exploiting the parallelism across the system [24]. Multiple shooting methods use parallelism across the steps by subdividing the time interval and solving a number of different problems on each interval concurrently [15,14].…”

Section: Parallel Solution Of Odesmentioning

confidence: 99%

Diagonal-Implicitly Iterated Runge–kutta Methods on Distributed Memory Machines

Rauber

Rünger

1999

Int. J. High Speed Comp.

Self Cite

View full text Add to dashboard Cite

We consider diagonal-implicitly iterated Runge-Kutta methods which are onestep methods for stiff ordinary differential equations providing embedded solutions for stepsize control. In these methods, algorithmic parallelism is introduced at the expense of additional computations. In this paper, we concentrate on the algorithmic structure of these Runge-Kutta methods and consider several parallel variants of the method exploiting algorithmic and data parallelism in different ways. Our aim is to investigate whether these variants lead to good performance on current distributed memory machines such as the Intel Paragon and the IBM SP2. As test application we use ordinary differential equations with dense and sparse right-hand side functions.

show abstract

Load balancing schemes for extrapolation methods

Cited by 23 publications

References 26 publications

Extrapolated Implicit-Explicit Time Stepping

Extrapolated Implicit-Explicit Time Stepping

Library Support for Hierarchical Multi-Processor Tasks

Diagonal-Implicitly Iterated Runge–kutta Methods on Distributed Memory Machines

Contact Info

Product

Resources

About