IETI - Isogeometric Tearing and Interconnecting

Area of Science:

• Computational mechanics
• Numerical analysis
• Computer-aided engineering

Background:

• Finite Element Tearing and Interconnecting (FETI) methods are effective for large-scale computational mechanics problems.
• Isogeometric Analysis (IGA) using Non-Uniform Rational B-splines (NURBS) offers exact geometry representation for complex domains.
• Existing methods face challenges in integrating advanced solvers with precise geometric modeling.

Purpose of the Study:

• To introduce the novel Isogeometric Tearing and Interconnecting (IETI) method.
• To combine the strengths of FETI solvers and IGA for enhanced computational efficiency.
• To address the challenges of simulating complex geometries with high fidelity.

Main Methods:

• Developed the IETI framework integrating FETI and IGA.
• Applied the method to Poisson and linearized elasticity model problems.
• Investigated subdomain coupling across matching and T-joint interfaces.
• Focused on constructing effective preconditioners for the interface problem's iterative solver.

Main Results:

• Demonstrated the feasibility of the IETI method for computational mechanics.
• Showcased successful coupling strategies for various interface types.
• Validated the performance of the proposed preconditioner.
• Presented computational experiments highlighting the method's efficiency.

Conclusions:

• The IETI method effectively merges FETI and IGA for advanced simulations.
• This approach provides a robust framework for handling complex geometries and large-scale problems.
• IETI offers a promising direction for future research in computational mechanics and solver design.