AI summary · arXiv: 2206.01541v1 · math.NA
A robust solution strategy for the Cahn-Larché equations
The essentials
- Authors propose a robust solution strategy for the Cahn-Larché equations
- Cahn-Larché equations model linearized elasticity in a medium with two elastic phases
- Equations combine Cahn-Hilliard regularized interface equation and linearized elasticity
- System is non-linearly coupled with a fourth-order term from the Cahn-Hilliard subsystem
- Authors propose a novel semi-implicit discretization in time to solve the system
- Standard convex-concave splitting method used for nonlinear double well potential
- Special treatment applied to elastic energy
- Discrete system shown to be equivalent to a convex minimization problem
- Alternating minimization approach proposed and proven to converge for this discrete system
- Numerical experiments demonstrate effectiveness of proposed solution strategy
- Approach outperforms standard methods for discretizing double well potentials and implicit evaluations of elasticity contributions
- Newly proposed discrete system better conditioned for linearization techniques
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