Fast linear solver using deflation for shape optimization

Abstract

Fast liner solvers for shape optimization using a deflation technique are discussed. The optimization method based on evolutionary algorithms such as genetic algorithm requires huge computational cost to evaluate many trial shapes. In this reason, a deflated preconditioned conjugate gradient (PCG) method is introduced so as to reduce the cost of finite element analysis which is used to evaluate the objective function. The deflation technique decomposes the solution into fast and slowly components. The slowly components can be solved by direct methods with low computational cost due to small dimensions. Therefore, the deflated PCC method can improve the convergence. Thus, the proposed method can reduce the computational cost. Numerical results show that the present method can improve the convergence and reduce the computational cost of optimizations of electromagnetic devices.