Benchmarking Approaches for the Multidisciplinary Analysis of Complex Systems Using a Taylor Series-Based Scalable Problem

In the practical use of multidisciplinary design optimization, the prevalent approach for the multidisciplinary analyses (MDA) is nonlinear block Gauss–Seidel iteration, which consists in solving each discipline in a sequential manner, and repeating this sequence until convergence. This approach is easy to implement but often exhibits slow convergence rates or does not converge at all. An alternative is to use approaches based on Newton’s method to solve the coupled system, also known as tightly coupled or monolithic approaches. Past work, especially in the field of fluid-structure interaction, shows that Newton-based tightly coupled approaches can be more efficient and robust than loosely coupled approaches for the analyses of coupled systems. With the computing power and methods currently available, it is expected that the application of MDA and MDO to systems of greater complexity in terms of coupling and number of disciplines will increase. This makes it important to compare loosely and tightly coupled approaches for complex systems. To address the lack of literature providing such comparisons, we use a novel and highly flexible Taylor series-based analytical scalable problem with OpenMDAO—an open-source framework for MDA and MDO—to compare coupled Newton and nonlinear block Gauss–Seidel approaches for complex systems. We find that assembly time of the linear systems involved, linear solver efficiency, and strength of coupling in the problem play a major role in determining which approach is more efficient for a given problem. We also observe that the coupled Newton approaches are more robust and scale better than the nonlinear block Gauss–Seidel approaches as the strength of coupling between components increases.