Enhancing Shell Simulation in SOFA Framework Using Advanced Angle-Based Deformation Energy Algorithms

Context

Shell elements are widely used in physics-based simulations to model thin, flexible structures like fabrics, membranes, and architectural components. These elements rely on approximations of the geometry using triangular meshes and bending models to represent deformation. Current implementations often face challenges with numerical stability, especially for stiff materials or under large deformations.

This project aims to address these challenges by leveraging the latest mathematical advancements in eigenanalysis and deformation gradient-based formulations. By implementing these algorithms, the enhanced Shell plugin will enable more stable, efficient, and realistic simulations for applications in computer graphics, robotics, biomechanics, and engineering.

Internship Description

This internship focuses on improving the shell simulation module in the SOFA framework, specifically the Shell plugin, by integrating advanced algorithms for angle-based deformation energy analysis, for instance, as introduced in the paper _”An Eigenanalysis of Angle-Based Deformation Energies”_ by Haomiao W. et al. (2023).

Responsibilities

• Study and understand the mathematical framework and algorithms for angle-based deformation energy eigenanalysis.
• Extend the SOFA Shell plugin to implement:
  1. Analytical Eigendecomposition for the energy Hessian to replace numerical methods.
  2. Eigenvalue Filtering to ensure semi-positive definite (SPD) stiffness matrices.
  3. Efficient Stencil-Based Deformation Gradient Calculation for hinge elements.
• Compare and benchmark the improved shell module against the existing implementation in terms of stability, performance, and accuracy.
• Optimize code performance for scalability to large-scale simulations.
• Write comprehensive documentation and unit tests for the new functionality.

Requirements

• Strong programming skills in C++
• Familiarity with the SOFA framework (optionnel)
• Solid background in numerical methods, linear algebra, and finite element methods.
• Knowledge of shell mechanics and experience with physics-based simulation is a plus.
• Ability to read and implement algorithms from research papers.
• Familiarity with Git for version control and collaborative development.

Learning Outcomes

• Hands-on experience implementing state-of-the-art algorithms in physics-based simulation.
• Understanding of advanced mathematical techniques like eigenanalysis and Hessian filtering.
• Experience contributing to open-source projects and real-world simulation tools.
• Skills in optimization and performance benchmarking for scientific applications.

How to Apply

Interested candidates are invited to send their CV, a cover letter, and any relevant work or project examples to yinoussa.adagolodjo@inria.fr and alexandre.bilger@inria.fr

If you are passionate about technological innovation and enjoy tackling modeling challenges in the medical field, we encourage you to apply and join our team in this impactful project.
Contract Duration: 6 months.