Efficient and Accurate Separable Models for Discretized Material Optimization: A Continuous Perspective Based on...

Area of Science:

• Engineering
• Computational Science
• Applied Mathematics

Background:

• Multi-material design optimization problems are often solved iteratively using simpler sub-problems.
• Convex separable first-order approximations are traditional and effective, leading to tools like the Method of Moving Asymptotes (MMA).

Purpose of the Study:

• To introduce and evaluate new separable approximations for multi-material design optimization.
• To assess the accuracy and computational efficiency of these novel models.
• To explore the relationship between models derived from different mathematical concepts.

Main Methods:

• Developing new separable approximations based on the Sherman-Morrison-Woodbury matrix identity and topological derivatives.
• Analyzing model accuracy and evaluation speed.
• Conducting numerical experiments to validate the proposed models.

Main Results:

• Two proposed models exhibit high accuracy in numerical experiments.
• Efficient evaluation of these models is possible after offline data precomputation.
• The study reveals a surprising connection between models from distinct mathematical origins.

Conclusions:

• The new separable approximations offer accurate and efficient solutions for multi-material design optimization.
• These models can prevent suboptimal design decisions.
• The findings highlight the potential of combining matrix identities and topological derivatives for optimization.