Development of software components for heterogeneous many-core architectures

1.1 Software development for heterogeneous architectures . . . . . . . . . . . . . . . . . . . 4 1.1.1 Test environments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 Heterogenous library design for PDE solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Component and concept design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.2 A matrix-free finite di↵erence component . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Model problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3.1 Heat conduction equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1.3.1.1 Assembling the heat conduction solver . . . . . . . . . . . . . . . . . . 14 1.3.1.2 Numerical solutions to the heat conduction problem . . . 16 1.3.2 Poisson equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 1.3.2.1 Assembling the Poisson Solver . . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.3.2.2 Numerical solutions to the Poisson problem . . . . . . . . . . . . 21 1.4 Optimization strategies for multi-GPU systems . . . . . . . . . . . . . . . . . . . . . . . . . . 22 1.4.1 Spatial domain decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.4.2 Parareal – Parallel time integration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.4.2.1 The Parareal algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.4.2.2 Computational complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.5 Conclusion and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

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