13: Anderson Acceleration #23
Description
Description
Implement Anderson acceleration to speed up convergence of nonlinear iterations. Useful for implicit time-stepping or steady-state wave problems.
Background
Anderson acceleration improves fixed-point iterations x_{k+1} = G(x_k) by mixing previous iterates:
x_{k+1} = Σᵢ αᵢ · G(x_{k-m+i})
where coefficients α are found by least-squares to minimize residual.
Tasks
- Implement Anderson mixing algorithm
- Store m previous iterates and residuals
- Solve least-squares for coefficients
- Apply mixing
- Integrate with time-stepping (for implicit schemes)
- Test on model problem
- Compare iteration counts: Picard vs Anderson
Acceptance Criteria
- Converges to same solution as Picard iteration
- Reduces iteration count by factor of 2-3x
- Robust for depth m = 3-5
- Works for various wave conditions
Parameters
Depth: m = 3-5 (number of previous iterates to use)
Regularization: small ε for least-squares stability