Advanced solution methods in topology optimization and shape sensitivity analysis

Investigates the efficiency of hybrid solution methods when incorporated into large-scale topology and shape optimization problems and to demonstrate their influence on the overall performance of the optimization algorithms. Implements three innovative solution methods based on the preconditioned conjugate gradient (PCG) and Lanczos algorithms. The first method is a PCG algorithm with a preconditioner resulted from a complete or an incomplete Cholesky factorization, the second is a PCG algorithm in which a truncated Neumann series expansion is used as preconditioner, and the third is a preconditioned Lanczos algorithm properly modified to treat multiple right-hand sides. The numerical tests presented demonstrate the computational advantages of the proposed methods which become more pronounced in large-scale and/or computationally intensive optimization problems.