Masters Thesis - TU Delft

Ω j , by the following rules:¯Ω = ∪ q j=1¯Ω j ∧ ∀ i≠j Ω i ∩Ω j = Ø (4.14)Let’s also denote Ω h and Ω hj , for the discretized domain and subdomains respectively. Afterthat we can introduce the deflation vector z j associated with the j-th subdomain as follows:z j (i) ={0, xi ∈ Ω h \Ω hj1, x i ∈ Ω hj. (4.15)After this step, we define Z = [z 1 z 2 . . . z q ]. This finish the construction.This method is strongly related to approaches known as Domain Decomposition Methods.4.2.2 Rigid Body ModesIn the recent research in the field of deflation, we can find another approach for choosing thedeflation vectors. In [13], we may find an introduction to the Rigid Body Modes used as theengine for the deflation vectors. The main idea is to set for the i-th deflation vector the i-thvector of the null space of A s , which is a submatrix created from the elements from the FEMdiscreatisation, which are composing the aggregate subdomains.20