A high-order partitioned solver for general multiphysics problems and its applications in optimization

TL;DR

This paper introduces a high-order, adjoint-based optimization framework for unsteady multiphysics problems that uses a partitioned solver to efficiently compute exact gradients, demonstrated through fluid-structure interaction applications.

Contribution

It develops a novel high-order, partitioned adjoint solver for multiphysics optimization, enabling accurate gradient computation in complex coupled systems.

Findings

Successfully applied to fluid-structure interaction problems

Achieved high-order accuracy and stability in adjoint computations

Demonstrated effectiveness in PDE-constrained optimization

Abstract

A high-order accurate adjoint-based optimization framework is presented for unsteady multiphysics problems. The fully discrete adjoint solver relies on the high-order, linearly stable, partitioned solver introduced in [1], where different subsystems are modeled and discretized separately. The coupled system of semi-discretized ordinary differential equations is taken as a monolithic system and partitioned using an implicit-explicit Runge-Kutta (IMEX-RK) discretization [2]. Quantities of interest (QoI) that take the form of space-time integrals are discretized in a solver-consistent manner. The corresponding adjoint equations are derived to compute exact gradients of QoI, which can be solved in a partitioned manner, i.e. subsystem-by-subsystem and substage-by-substage, thanks to the partitioned primal solver. These quantities of interest and their gradients are then used in the context of gradient-based PDE-constrained optimization. The present optimization framework is applied to two fluid-structure interaction problems: 1D piston problem with a three-field formulation and a 2D energy harvesting problem with a two-field formulation.