Date of download: 10/2/2017 Copyright © ASME. All rights reserved. Parallel Cell Mapping Method for Global Analysis of High-Dimensional Nonlinear Dynamical Systems1 J. Appl. Mech. 2015;82(11):111010-111010-12. doi:10.1115/1.4031149 Figure Legend: Global invariant set was found of the impact model. The subdivision processes in four different cellular space resolutions are presented to show the improvement of solution accuracy. Initial cell space partition is 7 × 7. Final cell space resolution reaches 189 × 189 with 3935 cells found as solutions. Computational time is 64.9844 s for sequential computing and 4.5573 s for parallel computing. (For the interpretation of color in all the figures, the reader is referred to the web version of the paper.)

Date of download: 10/2/2017 Copyright © ASME. All rights reserved. Parallel Cell Mapping Method for Global Analysis of High-Dimensional Nonlinear Dynamical Systems1 J. Appl. Mech. 2015;82(11):111010-111010-12. doi:10.1115/1.4031149 Figure Legend: Global properties of the impact model solved by the modified GCM analysis flow. Cell space partition is 189 × 189. Blue cells are the chaotic attractor, black are the unstable manifold, and red are the domain of attraction. Note the attractor and unstable manifold coincide with the invariant set shown in Fig. 1. Sequential computing takes 263.1347 s, while parallel computing takes 29.9928 s.

Date of download: 10/2/2017 Copyright © ASME. All rights reserved. Parallel Cell Mapping Method for Global Analysis of High-Dimensional Nonlinear Dynamical Systems1 J. Appl. Mech. 2015;82(11):111010-111010-12. doi:10.1115/1.4031149 Figure Legend: The attractors of the plasma model described in Eq. (31) in the cell space with 30 × 30 × 30 resolution. The four attractors occupy a quarter of the state space each and are symmetric with respect to the xz and yz plane. The CPU time of sequential computing for this example is 1418.9 s, while the parallel GCM analysis on GPU only takes 28.93 s. The parallel computing accelerates the computing by 49 times.

Date of download: 10/2/2017 Copyright © ASME. All rights reserved. Parallel Cell Mapping Method for Global Analysis of High-Dimensional Nonlinear Dynamical Systems1 J. Appl. Mech. 2015;82(11):111010-111010-12. doi:10.1115/1.4031149 Figure Legend: The domain of attraction of the first PG of the plasma model. Red cells are the attractor while blue ones are the corresponding domain of attraction. The cells in the domain occupy a quarter of the 3D state space.

Date of download: 10/2/2017 Copyright © ASME. All rights reserved. Parallel Cell Mapping Method for Global Analysis of High-Dimensional Nonlinear Dynamical Systems1 J. Appl. Mech. 2015;82(11):111010-111010-12. doi:10.1115/1.4031149 Figure Legend: Number of cells to be processed at each iteration of rolling cut subdivision of one dimension at a time. We chose to stop the subdivision when the number starts to decrease at the 16th iteration.

Date of download: 10/2/2017 Copyright © ASME. All rights reserved. Parallel Cell Mapping Method for Global Analysis of High-Dimensional Nonlinear Dynamical Systems1 J. Appl. Mech. 2015;82(11):111010-111010-12. doi:10.1115/1.4031149 Figure Legend: The attractor of the 6D Lorenz system obtained by the SCM–GCM hybrid method and post-processing with interpolation. Blue dots are the central points of the cells representing the attractor projected to the 3D space. Red dots are the interpolated points. The familiar butterfly shape can be seen from the low-dimensional projection.

Date of download: 10/2/2017 Copyright © ASME. All rights reserved. Parallel Cell Mapping Method for Global Analysis of High-Dimensional Nonlinear Dynamical Systems1 J. Appl. Mech. 2015;82(11):111010-111010-12. doi:10.1115/1.4031149 Figure Legend: Two-dimensional projections of the attractor of the 6D Lorenz system. Blue dots are the centers of the cells in the invariant set. Red dots showing the fine structure of the attractor are generated with interpolation.

Date of download: 10/2/2017 Copyright © ASME. All rights reserved. Parallel Cell Mapping Method for Global Analysis of High-Dimensional Nonlinear Dynamical Systems1 J. Appl. Mech. 2015;82(11):111010-111010-12. doi:10.1115/1.4031149 Figure Legend: The relationship between the number of sampled points and the Hausdorff distance of the invariant set of the 6D Lorenz system is obtained by the interpolation scheme to the reference set. The interpolation scheme appears to be insensitive to the number of sampled points.