Stefan Kiel, Ekaterina Auer, Andreas Rauh
In this paper, we discuss parameter identification for models based on ordinary differential equations in the context of solid oxide fuel cells. In this case, verified methods (e.g. interval analysis), which provide a guarantee of correctness for the computed result, can be of great help for dealing with the appearing uncertainty and for devising accurate […]
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Chen Huang, Bailey Miller, Frank Vahid, Tony Givargis
Physical system models that consist of thousands of ordinary differential equations can be synthesized to field-programmable gate arrays (FPGAs) for highly-parallelized, real-time physical system emulation. Previous work introduced synthesis of custom networks of homogeneous processing elements, consisting of processing elements that are either all general differential equation solvers or are all custom solvers tailored to […]
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Tomohiro Okuyama
The graphics processing unit (GPU) is recently used as a massively parallel processor to speed up general computation. However, the GPU can decrease the performance of irregular computation, because the GPU is based on the single instruction, multiple data (SIMD) architecture. The irregular computations here are conditional branches and memory accesses, which vary the behavior […]
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Matthew Grossman
The development of increasingly powerful and low cost massively parallel processors, known as GPUs, has created new opportunities for high speed and high precision computational work in physics. GPUs are extremely well suited to solving computationally intense problems at speeds much greater than traditional processors. They are now found in most personal computers, with research […]
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Sudeep Dasari, David Murphy, Colin Redman
Tornadoes such as Joplin, Mo (2011), Spencer, SD (1998), and Dallas, Texas (1957) induce extremely high wind velocities that devastate structures and lift off large objects in their path. Typically, a tornado takes up to an hour to materialize in the form of a narrow axisymmetric vortex and sustains that structure for 10-20 minutes after […]
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A. Gorecki
The modeling of ion-transport through biological membranes is important for understanding many life processes. The transmembrane potential and ion concentrations in the stationary state can be measured in in-vivo experiments. They can also be simulated within membrane models. Here we consider a basic model of ion transport that describes the time evolution of ion concentrations […]
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Cyril Fischer
The presented contribution maps the possibilities of exploitation of the massive parallel computational hardware (namely GPU) for solution of the initial value problems of ordinary differential equations. Two cases are discussed: parallel solution of a single ODE and parallel execution of scalar ODE solvers. Whereas the advantages of the special architecture in the case of […]
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Denis Demidov, Karsten Ahnert, Karl Rupp, Peter Gottschling
We present a comparison of several modern C++ libraries providing high-level interfaces for programming multi- and many-core architectures on top of CUDA or OpenCL. The comparison focuses on the solution of ordinary differential equations and is based on odeint, a framework for the solution of systems of ordinary differential equations. Odeint is designed in a […]
Bruno Gouvea de Barros, Rafael Sachetto Oliveira, Wagner Meira Jr., Marcelo Lobosco, Rodrigo Weber dos Santos
Key aspects of cardiac electrophysiology, such as slow conduction, conduction block, and saltatory effects have been the research topic of many studies since they are strongly related to cardiac arrhythmia, reentry, fibrillation, or defibrillation. However, to reproduce these phenomena the numerical models need to use subcellular discretization for the solution of the PDEs and nonuniform, […]
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N. Kulabukhova
Matrix formalism is a map integration method for ODE solving. It allows to present solution of the system as sums and multiplications of 2-indexes numeric matrix. This approach can be easy implement in parallel codes. As the most natural for matrix operation GPU architecture has been chosen. The set of the methods for beam dynamics […]
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Lars Grune, Thomas U. Jahn
We consider the problem of computing reachable sets of ODE-based control systems parallely on CUDA hardware. To this end, we modify an existing algorithm based on solving optimal control problems. The idea is to simplify the optimal control problems to pure feasibility problems instead of minimizing an objective function. We show that an interior point […]
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Matthias Korch
The solution of initial value problems of large systems of ordinary differential equations (ODEs) is computationally intensive and demands for efficient parallel solution techniques that take into account the complex architectures of modern parallel computer systems. This article discusses implementation techniques suitable for ODE systems with a special coupling structure, called limited access distance, which […]
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