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1. Introduction NRL has ongoing interest and research in predictive design and optimization of structural acoustic systems. Over the years, NRL has developed accurate and robust finite-element-based methods to compute structural-acoustic quantities of interest (QoI) for specific material and geometric configuration of a system. For truly predictive designs that meet one or more performance criteria, one needs mathematically robust optimization approaches. A key ingredient in such methods is the sensitivities of the QoI to specific material and geometric parameters that govern a design. The ability to compute these sensitivities can also be used to compute the error in estimating the QoIs, and drive goal-based mesh adaptivity.

In order to accelerate ongoing NRL efforts in this area, NRL is looking to acquire computational capability from the supplier, who has unique expertise in this area. During the previous years of this effort the work done involved:

a. Developing a structural acoustics finite element formulation for computing sensitivities with respect to material properties for interior and exterior structural acoustics problems.

b. Implementing this formulation within Fenics, and open-source finite element code.

c. Utilizing the ability to compute material sensitivities to solve optimal design problems.

d. Developing initial ideas on using sensitivities to estimate errors in QoIs and embedding prior information in the optimization process.

The initial capability needs to be expanded as described below.

2. Required capabilities

a. Integration of the Capstone platform for geometry and mesh generation to the Fenics-based optimization tool in order to solve problems with complex geometry in three-dimensions.

b. Developing capability to compute sensitivities with respect to geometrical parameters in addition to material parameters.

c. Account for manufacturing feasibility considerations when developing optimal design solutions. It is anticipated that this will be done by embedding prior information in the optimization problem via ML techniques like Generative Adversarial Networks.

d. Estimate the error in QoIs and its spatial variation. The goal would be to implement a method for estimating an error-driven mesh size field that could be used to drive mesh adaptivity to ensure more accurate forward solutions.

3. Deliverables

a. A well-documented finite element software library with the components described in Section 2.

b. Self-explanatory example problems using the software library in 3a.