Optimization-Based Strong Coupling Procedure for Partitioned Analysis

Abstract

The concept of partitioning a complex engineering problem into smaller, manageable components and investigating each individual component autonomously has been in use for many decades. Such partitioning approaches, however, rely on strong and occasional unwarranted assumptions regarding the interactions among different engineering components. Fluid and structure interaction, soil and structure interaction, and human and structure interaction are but a few of the many such partitioned analyses commonly needed in civil engineering applications. Recently, there has been a growing interest in combining the expertise developed separately in traditionally distinct fields to obtain a holistic treatment of engineering problems. Such holistic treatment would ultimately yield not only more realistic and accurate analyses of coupled systems but also improved optimality in engineering designs. This growing interest has resulted in development of mathematical coupling procedures for conjoining multiple, separately developed, single-solver numerical models along their interfaces. The present manuscript contributes to the field of partitioned analysis by introducing a novel mathematical coupling procedure based on the minimization of an objective function consisting of coupling conditions. The authors’ approach to coupling implements optimization techniques and is observed to eliminate the divergence issues that may be encountered with iterative coupling methods. The proposed optimization-based coupling scheme is compared against the well-known block Gauss-Seidel (BGS) iteration method and considers two aspects: the accuracy of the coupled model predictions and the convergence of the coupled parameters. The comparison is completed for three case studies with increasing complexity: a linear set of equations, polynomials with random coefficients, and a linear dynamic system.