Systematic methods to design complex systems are required to fully realize the vast space of possible designs afforded by advanced manufacturing (AM) technologies. The complexity comes from two sources: design and physics. Design complexity refers to the intricate shapes and material layouts made possible by today's AM, including structural composites with detailed morphologies. Design complexity also refers to the metrics considered to, for example, optimize a structure subjected to local strength constraints as well as global stiffness and mass considerations. Physics complexity comes from the continuum finite element simulations used to predict design performance, i.e., to evaluate cost and constraint functions driving optimization. These simulations approximate the solutions of partial differential equations that contain complicated nonlinearities, transients, multiple scales, multiple physics, and uncertainty. Design problems are nonlinear, requiring iterations to traverse the design space and solving finite element equations for each new design. Design degrees-of-freedom (DOF) and physics DOF exceed one billion, therefore, our methods require efficient high-performance computing (HPC) optimization algorithms.
Our primary goal was to develop and implement HPC, gradient-based optimization algorithms to design immensely complex systems. We relied on efficient nonlinear programming (NLP) algorithms to efficiently traverse the design space and adjoint methods to compute gradients of the cost and constraint functions required by the NLP algorithms. Our algorithms were implemented in the newly developed HPC Livermore Design Optimization (LiDO) software and were applied to solve mechanical, metameterial, and electromagnetic design problems. The LiDO code contains over 55,000 new lines of C++ code to link to existing Lawrence Livermore National Laboratory HPC libraries, compute cost and constraint functions, and implement the adjoint gradient computations in a fully parallelized manner. Livermore's HPC Solver for Optimization library is another direct outcome of our work.
LiDO leveraged Livermore's core competencies in high-performance computing, simulation, and data science and the Laboratory's earlier investments in HPC libraries, which hastened the LiDO development time. The project supports the Laboratory Director's Initiative in rapid, cost-effective advanced materials and manufacturing. LiDO’s capabilities expand the range of physics and applications within Livermore's optimization portfolio and can help solve design problems across the Laboratory’s mission space. Other organizations, including the NNSA, have expressed interest in applying LiDO to their programs.
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