Lawrence Livermore National Laboratory

Daniel Tortorelli


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.

Impact on Mission

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.

Publications, Presentations, Etc.

Barbarosie, C., et al. 2017. "On Domain Symmetry and Its Use in Homogenization." Computer Methods in Applied Mechanics and Engineering 320:1–45. LLNL-JRNL-690921.

Carlberg, K., et al. 2018. "Conservative Model Reduction for Finite-Volume Models." Journal of Computational Physics 371:280–314. LLNL-JRNL-742522.

Choi, Y. and K. Carlberg. 2019. "Space-Time Least-Squares Petrov-Galerkin Projection for Nonlinear Model Reduction." SIAM Journal on Scientific Computing 41 (1):A26–A58. LLNL-POST-734301.

Dilgen, S., et al. 2018. "Density Based Topology Optimization of Turbulent Flow Heat Transfer Systems." Structural and Multidisciplinary Optimization 57 (5):1905–1918. LLNL-JRNL-747713.

Fernandez, F., et al. 2019. "Optimal Design of Fiber Reinforced Composite Structures and Their Direct Ink Write Fabrication." Computer Methods in Applied Mechanics and Engineering 353:277–307. LLNL-POST-755896.

Fernandez, F. and D. Tortorelli. 2018. "Semi-Analytical Sensitivity Analysis for Nonlinear Transient Problems." Structural and Multidisciplinary Optimization 58 (6):2387–2410. LLNL-JRNL-746929.

Keshavarzzadeh, V., et al. 2019. "Shape Optimization Under Uncertainty for Rotor Blades of Horizontal Axis Wind Turbines." Computer Methods in Applied Mechanics and Engineering 354:271–306. LLNL-JRNL-701297.

Lian, H., et al. 2017. "Combined Shape and Topology Optimization for Minimization of Maximal Von Mises Stress." Structural and Multidisciplinary Optimization 55 (5):1541–1557. LLNL-JRNL-708997.

Najafi, A., et al. 2017. "Shape Optimization Using a NURBS-Based Interface-Enriched Generalized FEM." International Journal for Numerical Methods in Engineering 111 (10):927–954. LLNL-JRNL-708998.

Petra, C. 2019. "A Memory-Distributed Quasi-Newton Solver for Nonlinear Programming Problems with a Small Number of General Constraints." Journal of Parallel and Distributed Computing 133:337–348. LLNL-JRNL-739001.

Petra, C., et al. 2019. "A Structured Quasi-Newton Algorithm for Optimizing with Incomplete Hessian Information." SIAM Journal on Optimization 29 (2):1048–1075. LLNL-JRNL-745068.

Saito, Y., et al. 2019. "Experimental Validation of an Additively Manufactured Stiffness-Optimized Short-Fiber Reinforced Composite Clevis Joint." Experimental Mechanics 59 (6):859–869. LLNL-JRNL-764135.

Salazar de Troya, M. and D. Tortorelli. 2018. "Adaptive Mesh Refinement in Stress-Constrained Topology Optimization." Structural and Multidisciplinary Optimization 58 (6):2369–2386. LLNL-JRNL-748566.

Wallin, M., et al. 2018. "Stiffness Optimization of Non-Linear Elastic Structures." Computer Methods in Applied Mechanics and Engineering 330:292-307. LLNL-JRNL-731767.

Watts, S., et al. 2019. "Simple, Accurate Surrogate Models of the Elastic Response of Three-Dimensional Open Truss Micro-Architectures with Applications to Multiscale Topology Design." Structural and Multidisciplinary Optimization. LLNL-JRNL-758077.

Watts, S. and D. Tortorelli. 2017. "A Geometric Projection Method for Designing Three-Dimensional Open Lattices with Inverse Homogenization." International Journal for Numerical Methods in Engineering 112 (11):1564-1588. LLNL-JRNL-701297.

——— . 2017. "Optimality of Thermal Expansion Bounds in Three Dimensions." Extreme Mechanics Letters 12:97–100. LLNL-JRNL-667959.

White, D. and A. Voronin. 2019. "A Computational Study of Symmetry and Well-Posedness of Structural Topology Optimization." Structural and Multidisciplinary Optimization 59 (3):759–766. LLNL-JRNL-761-457.

White, D., et al. 2019. "Multiscale Topology Optimization Using Neural Network Surrogate Models." Computer Methods in Applied Mechanics and Engineering 346:1118–1135. LLNL-JRNL-760619.