Optimal Design by Adaptive Mesh Refinement on Shape Optimization of Flow Fields Considering Proper Orthogonal Decomposition

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical optimization and variational techniques (65K10) Numerical computation of solutions to systems of equations (65H10) Navier-Stokes equations for incompressible viscous fluids (76D05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Navier-Stokes equations (35Q30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50) Optimization of shapes other than minimal surfaces (49Q10) Computer system organization (68M99) Sensitivity analysis for optimization problems on manifolds (49Q12)