Fully Differentiable Boundary Element Solver for Hydrodynamic Sensitivity Analysis of Wave-Structure Interactions

Authors

Kapil Khanal^a,b, Carlos A. Michelén Ströfer^b, Matthieu Ancellin^c, Maha Haji^a

Affiliations

• ^aCornell University
  Ithaca, NY 14850, USA
• ^bSandia National Laboratories
  Albuquerque, NM 87123, USA
• ^cEurobios Mews Labs
  Paris, France

🌟 Research Highlights

• 📚 Derivation and discussion of the discrete adjoint method for the boundary integral equations.
• 💻 Review and implementation of a differentiable boundary element solver for marine hydrodynamics in Julia.
• 🌊 Exact gradient calculation for a pair of floating hemispheres with respect to their dimensions, separation distance, and wave environment.
• ⚡ Mechanical power optimization for a pair of wave energy converters using exact gradients.

Fully-differentiable boundary element solver for marine hydrodynamics. This new solver implements both direct and indirect boundary element formulations and uses two green's function expression, Wu et al, and Delhommeau's varying in their accuracy and speed.

⚠️ Note: This package is work in progress 🚧 and a separate public release of the package will be done in the future. This current state of the package contains necessary code to replicate the paper 📄. It will go through a significant change in its API for users in future iterations.

Repository: MarineHydro.jl

📂 Folder Structure

• 📁 .github/workflows
  Contains workflow files for automated tasks, such as continuous integration (CI).

• 📊 paper
  Includes plots and data generated for the paper.

• 📜 src
  Source code files for the BEM.jl package, including the main functionality.

• 🧪 test
  Contains test files and resources to verify the functionality of the source code.

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🚀 How to Run the Code

1. Install Julia
   Ensure you have Julia installed on your system. You can download it from the JuliaLang website.

2. Clone the Repository
   Open a terminal and run:

   git clone https://github.com/symbiotic-engineering/MarineHydro.jl.git
   cd MarineHydro.jl
   
   

3. Install Dependencies
   Start Julia from the terminal in the project directory and run the following:

   using Pkg
   Pkg.activate(".")
   Pkg.instantiate()

   You may need to configure PyCall. Note: Running tests/ automatically install capytaine and uses it.

4. Configure PyCall

   ENV["PYTHON"] = "/path/to/capytaine_env/bin/python" # run 'which python' in your terminal for this
   

5. Using the BEM Module
   Load the module in your Julia session:

using BEM
using PyCall
# import your capytaine mesh
cpt = pyimport("capytaine")
radius = 1.0 #fixed
resolution = (10, 10)
cptmesh = cpt.mesh_sphere(name="sphere", radius=radius, center=(0, 0, 0), resolution=resolution) 
cptmesh.keep_immersed_part(inplace=true)

# declare it Julia mesh
mesh = Mesh(cptmesh)  
ω = 1.03
ζ = [0,0,1] # HEAVE: will be more verbose in future iteration. define it again even if defined in Capytaine.
F = DiffractionForce(mesh,ω,ζ)
A,B = calculate_radiation_forces(mesh,ζ,ω)

6. Differentiability : For differentiability with respect to mesh dimension, use paper/MeshGradients_singlebody.jl Differentiability needs an AD engine: use Zygote

using Zygote
A_w_grad, = Zygote.gradient(w -> calculate_radiation_forces(mesh,ζ,w)[1],ω)