New variants of deflation techniques for bubbly flow problems
Jinyu Tang, C. Vuik · Data Archiving and Networked Services (DANS) · 2006
Abstract. For various applications, it is well-known that deflated ICCG is an efficient method for solving linear systems with invertible and singular co-efficient matrix. This deflated ICCG with subdomain deflation vectors is used by us to solve linear systems with singular coefficient matrix, arising from a discretization of the Poisson equation with Neumann boundary conditions and discontinuous coefficients. However, we have not explained the fact that the use of subdomain deflation vectors is effective. In this paper, we investigate this by doing some perturbed eigenvector analysis and we make it plausible that the use of subdomain deflation vectors is beneficial for the number of iterations and the amount of computational time. Moreover, we introduce new variants of the deflation technique which can deal with bubbly flow problems and with two-phase flow problems in general. The most simple variant is the so-called levelset deflation technique which chooses deflation vectors corresponding to the bubbles in the domain. Another variant is to combine the subdomain and levelset deflation technique which