Scalable Parallel RK Solvers for ODEs Derived by the Method of Lines

Korch, Matthias; Rauber, Thomas

doi:10.1007/978-3-540-45209-6_113

Cited by 8 publications

(26 citation statements)

References 12 publications

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“…This implementation strategy is suitable for ODE systems with limited access distance. It has been derived from the pipelining scheme presented in [29,30,31] by an overlapping of vectors. The implementation strategy proposed herein provides a higher locality of memory references and requires less storage space than our previous implementations and other implementations proposed in related works.…”

Section: Discussionmentioning

confidence: 99%

“…, f n ) where the components of the argument vector accessed by each component function f j lie within a bounded index range near j. In the following, we review the pipelining approach proposed in [29,30,31], which exploits this property of the ODE system and supports arbitrary RK coefficients.…”

Section: Exploiting Limited Access Distance Tomentioning

confidence: 99%

“…In this paper, we reconsider a pipelining approach suggested, initially, to improve locality and scalability of embedded RK implementations in [30] from this perspective. As we will show in the following sections, for IVPs with a special dependence pattern, the storage space can be reduced by an overlapped memory layout of the data structures such that only one enlarged register of dimension n can be (re-)used for all stage computations.…”

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confidence: 99%

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Parallel Low-Storage Runge—Kutta Solvers for ODE Systems with Limited Access Distance

Korch

Rauber

2010

The International Journal of High Performance Computing Applica

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Section: Discussionmentioning

confidence: 99%

Section: Exploiting Limited Access Distance Tomentioning

confidence: 99%

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confidence: 99%

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Parallel Low-Storage Runge—Kutta Solvers for ODE Systems with Limited Access Distance

Korch

Rauber

2010

The International Journal of High Performance Computing Applica

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“…For work on parallel differential equation solver implementations in a broader context than Modelica see for instance [84,62,40,83].…”

Section: Related Research In Other Research Groupsmentioning

confidence: 99%

Contributions to Simulation of Modelica Models on Data-Parallel Multi-Core Architectures

Stavåker

2015

Linköping Studies in Science and Technology. Dissertations

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Modelica is an object-oriented, equation-based modeling and simulation language being developed through an international effort by the Modelica Association. With Modelica it is possible to build computationally demanding models; however, simulating such models might take a considerable amount of time. Therefore techniques of utilizing parallel multi-core architectures for faster simulations are desirable. In this thesis the topic of simulation of Modelica on parallel architectures in general and on graphics processing units (GPUs) in particular is explored. GPUs support code that can be executed in a data-parallel fashion. It is also possible to connect and run several GPUs together which opens opportunities for even more parallelism. In this thesis several approaches regarding simulation of Modelica models on GPUs and multi-core architectures are explored.In this thesis the topic of expressing and solving partial differential equations (PDEs) in the context of Modelica is also explored, since such models usually give rise to equation systems with a regular structure, which can be suitable for efficient solution on GPUs. Constructs for PDE-based modeling are currently not part of the standard Modelica language specification. Several approaches on modeling and simulation with PDEs in the context of Modelica have been developed over the years. In this thesis we present selected earlier work, ongoing work and planned work on PDEs in the context of Modelica. Some approaches detailed in this thesis are: extending the language specification with PDE handling; using a software with support for PDEs and automatic discretization of PDEs; and connecting an external C++ PDE library via the functional mockup interface (FMI).Finally the topic of parallel skeletons in the context of Modelica is explored. A skeleton is a predefined, generic component that implements a common specific pattern of computation and data dependence. Skeletons provide a high degree of abstraction and portability and a skeleton can be customized with user code. Using skeletons with Modelica opens up the possibility of executing heavy Modelica-based matrix and vector computations on multi-core architectures. A working Modelica-SkePU library with some minor necessary compiler extensions is presented.This work has been supported by the European ITEA2 OPENPROD project (Open Model-Driven Whole-Product Development and Simulation Environment), the European ITEA3 MODRIO project (Model Driven Physical Systems Operation) and by the National Graduate School of Computer Science (CUGS) 1 2 Populärvetenskaplig sammanfattningModelicaär ett objektorienterat, ekvationsbaserat modellerings-och simuleringsspråk som utvecklas via den internationella organisationen the Modelica Association. Med Modelicaär det möjligt att bygga beräkningskrävande modeller vilket kan leda till långa simuleringstider. Därförär metoder för att utnyttja parallella flerkärniga arkitekturer för snabbare simuleringarönskvärda. I denna avhandling utforskas området simulering av Modelicamod...

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“…Generation of parallel executable code from Modelica models has been a research topic for several years at our research group, see for instance [1], [5]. For other work on parallel differential equation solver implementations, see for instance [10], [11], [4].…”

Section: Introductionmentioning

confidence: 99%

Parallel simulation of equation-based models on CUDA-enabled GPUs

Östlund

Stavåker

Fritzson

2010

Proceedings of the 9th Workshop on Parallel/High-Performance Object-Oriented Scientific Computing

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Our contributions with this work are methods and a prototype implementation for compiling and executing a limited set of equation-based mathematical models (written in the object-oriented equation-based modeling language Modelica) on CUDA-enabled GPUs. We look at methods of finding parallelism in Modelica models, that can be used on the massively parallel CUDA architecture. The methods have been implemented in a new back-end module of the OpenModelica compiler (an open-source Modelica compiler). This paper shows that it is possible to automatically generate simulation code for pure continuous-time models that can be reduced to an ordinary differential equation system without algebraic loops and where the initial values of all variables and parameters are known at compile time. It is possible to get some speedup compared with simulation on a single CPU core, a (approximated) relative speedup of 4.6 was for instance obtained for one model.

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Scalable Parallel RK Solvers for ODEs Derived by the Method of Lines

Cited by 8 publications

References 12 publications

Parallel Low-Storage Runge—Kutta Solvers for ODE Systems with Limited Access Distance

Parallel Low-Storage Runge—Kutta Solvers for ODE Systems with Limited Access Distance

Contributions to Simulation of Modelica Models on Data-Parallel Multi-Core Architectures

Parallel simulation of equation-based models on CUDA-enabled GPUs

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