Graphical Processing Units (GPUs) have been a disruptive technology and, over the last decade, there has been a growing interest in the use of GPUs for non-graphical applications, which is the main topic of this research. This project investigates scientific computing methods by means of both explicit and implicit algorithms by adopting representative problems for each case, namely, fragmentation and topology optimization, respectively. The intellectual merit of the research consists of establishing a conceptual framework to map fragmentation and topology optimization simulations to GPUs, creating a novel special-purpose topological data structure tailored for adaptive finite element meshes on GPU platforms with fast global-memory access.

In terms of fragmentation, we created a framework for dynamic adaptation of the mesh in the GPU, in a consistent fashion, by inserting cohesive elements on fractured facets (duplicating nodes and updating connectivity ‘on the fly’). We developed an effective nodal update scheme using gather and scatter techniques necessary for GPU parallelization. Gather techniques were employed to insert cohesive elements while scattering techniques, based on coloring, were employed to compute nodal stress, nodal mass, internal forces, and cohesive forces. We developed parallel techniques to map fragmentation algorithms to GPUs, such as splitting of kernels into simpler ones, distributing jobs among threads, taking advantage of memory coalescence (consecutive threads reading consecutive memory addresses), and using texture memory to increase kernel performance. For instance, the computation of the cohesive forces kernel uses one thread per element for n colors. It is decomposed as follows: (1) computation of cohesive separation kernel (one thread per cohesive element); (2) computation of cohesive traction kernel (three threads per cohesive element); and (3) computation of cohesive force kernel (one thread per element for n colors).

In terms of topology optimization, we have presented a topology optimization implementation that uses polygonal finite elements implemented in C++ language and in CUDA. It provides several features to handle the computational cost associated with the use of large-scale polygonal meshes. The modular feature provides an easy way to modify and extend the code to use different analysis routines without changing the topology optimization formulation. We presented different types of linear solvers that can be used in the finite element analysis.

In terms of broader impacts, the scale of the problems addressed in this research lead to new insights into topology optimization and fragmentation, as documented in archival publications. Moreover, concepts developed from this research were adopted into the curriculum at UIUC, GATech and Stanford Universities. Educational and research findings were disseminated on the PI’s website and by means of other dissemination venues (conferences, seminars, lectures, journal papers, etc).

Last Modified: 06/05/2017
Modified by: Glaucio Paulino