Chapter

Numerical Computations with GPUs

pp 125-157

Date:

Solving Ordinary Differential Equations on GPUs

  • Karsten AhnertAffiliated withAmbrosys GmbH Email author 
  • , Denis DemidovAffiliated withKazan Branch of Joint Supercomputer Center, Russian Academy of Sciences
  • , Mario MulanskyAffiliated withMax-Planck Institute for the Physics of Complex SystemsTU-Dresden, Institute for Theoretical Physics

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Abstract

Ordinary Differential Equations (ODEs) are a fundamental mathematical tool to model physical, biological or chemical systems, and they are widely used in engineering, economics and social sciences. Given their vast appearance, it is of crucial importance to develop efficient numerical routines for solving ODEs that employ the computational power of modern GPUs. Here, we present a high-level approach to compute numerical solutions of ODEs by developing a generic implementation of the most common algorithms and combining this with modern C\(++\) libraries like VexCL and Thrust. Our approach is based on generic programming and results in highly scalable and easy-to-use source code.