Massive Parallel Implementation of ODE Solvers

Cyril Fischer
Institute of Theoretical and Applied Mechanics AS CR, v.v.i. Prosecka 76, Prague 9, Czech Republic
Programs and Algorithms of Numerical Matematics 16, 2013


   author={Chleboun, J and Segeth, K and {v{S}}{i}stek, J and Vejchodsk{`y}, T},

   journal={Programs and Algorithms of Numerical Mathematics 16},




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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 a single ODE are problematic, repeated solution of a single ODE for different data can profit from the parallel architecture. However, special algorithms have to be used even in the latter case to avoid code divergence between individual computational threads. The topic is illustrated on several examples.
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