An asynchronous solver for systems of ODEs linked by a directed tree structure

Scott J Small; Laurent O Jay; Ricardo Mantilla; Rodica Curtu; Luciana K Cunha; Morgan Fonley; Witold F Krajewski

doi:10.1016/j.advwatres.2012.10.011

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An asynchronous solver for systems of ODEs linked by a directed tree structure

Journal article

Peer reviewed

An asynchronous solver for systems of ODEs linked by a directed tree structure

Scott J Small, Laurent O Jay, Ricardo Mantilla, Rodica Curtu, Luciana K Cunha, Morgan Fonley and Witold F Krajewski

Advances in water resources, Vol.53, pp.23-32

03/2013

DOI: 10.1016/j.advwatres.2012.10.011

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Abstract

► Introduces a numerical solver for systems of ODEs linked by a tree structure. ► The emphasized use is for solving hillslope-link river basin models. ► Asynchronous integrators are used for to improve performance. ► A parallel distributed memory implementation is proposed. This paper documents our development and evaluation of a numerical solver for systems of sparsely linked ordinary differential equations in which the connectivity between equations is determined by a directed tree. These types of systems arise in distributed hydrological models. The numerical solver is based on dense output Runge–Kutta methods that allow for asynchronous integration. A partition of the system is used to distribute the workload among different processes, enabling a parallel implementation that capitalizes on a distributed memory system. Communication between processes is performed asynchronously. We illustrate the solver capabilities by integrating flow transport equations for a ∼17,000km2 river basin subdivided into 305,000 sub-watersheds that are interconnected by the river network. Numerical experiments for a few models are performed and the runtimes and scalability on our parallel computer are presented. Efficient numerical integrators such as the one demonstrated here bring closer to reality the goal of implementing fully distributed real-time flood forecasting systems supported by physics based hydrological models and high-quality/high-resolution rainfall products.

Distributed memory

Asynchronous communication

Hillslope-link river basin model

Tree structure

Asynchronous integrator

Details

Title: Subtitle: An asynchronous solver for systems of ODEs linked by a directed tree structure
Creators: Scott J Small - IIHR-Hydroscience & Engineering, The University of Iowa, Iowa City, IA 52242, USA
Laurent O Jay - Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA
Ricardo Mantilla - IIHR-Hydroscience & Engineering, The University of Iowa, Iowa City, IA 52242, USA
Rodica Curtu - Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA
Luciana K Cunha - IIHR-Hydroscience & Engineering, The University of Iowa, Iowa City, IA 52242, USA
Morgan Fonley - Department of Mathematics, The University of Iowa, Iowa City, IA 52242, USA
Witold F Krajewski - IIHR-Hydroscience & Engineering, The University of Iowa, Iowa City, IA 52242, USA
Resource Type: Journal article
Publication Details: Advances in water resources, Vol.53, pp.23-32
DOI: 10.1016/j.advwatres.2012.10.011
ISSN: 0309-1708
eISSN: 1872-9657
Publisher: Elsevier Ltd
Language: English
Date published: 03/2013
Academic Unit: Civil and Environmental Engineering; Iowa Neuroscience Institute; IIHR--Hydroscience and Engineering; Mathematics
Record Identifier: 9983985823902771

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