Locally-synchronous, iterative solver for Fourier-based homogenization

Abstract We use the algebraic orthogonality of rotation-free and divergence-free fields in Fourier space to derive solution a class linear homogenization problems as large system. The effective constitutive tensor constitutes only small part vector. Therefore, we propose synchronous local iterative method that is capable efficiently compute single component If convergence solver ensured, i.e., system matrix positive definite diagonally dominant, it outperforms standard direct solvers complete solution. It has been found for larger phase contrasts problem, lost, one needs resort other solvers. discuss system’s properties advantages well drawbacks presented approach.