New Preconditioners with Two Variable Relaxation Parameters for the Discretized Time-Harmonic Maxwell Equations in Mixed Form

Table 2

Iteration counts for different 𝑘² and 𝜂, using BiCGSTAB with the preconditioner 𝑀_{𝑘,𝜂,𝜀}, and 𝑚+𝑛=16129. The iteration was stopped once ‖𝑟^(𝑘)‖/‖𝑟⁽⁰⁾‖≤5×10⁻¹⁰.

𝜂	𝑘^2	0.1	0.2	0.5	1	2	3	4	5
𝑘^2+0.001	Iter	2	2	2.5	2.5	3	3.5	4	4.5
𝑘^2+0.01	Iter	2	2	2.5	2.5	3	3.5	4	4.5
𝑘^2+0.1	Iter	2	2	2.5	2.5	3	3.5	4	4.5
𝑘^2+0.25	Iter	2.5	2.5	2.5	2.5	3.5	3.5	4	4.5
𝑘^2+0.5	Iter	2.5	2.5	2.5	2.5	3.5	4	4	4.5
𝑘^2+1	Iter	2.5	2.5	2.5	3	3.5	4	4	4.5
𝑘^2+1.5	Iter	2.5	2.5	3	3	3.5	4	4.5	4.5
𝑘^2+2	Iter	3	3	3	3.5	3.5	4	4.5	4.5
𝑘^2+5	Iter	3.5	3.5	3.5	4	4.5	4.5	4.5	5
𝑘^2+15	Iter	4.5	5	5	5	5	5.5	5.5	5.5
𝑘^2+30	Iter	5.5	5.5	5.5	6	6	6	6	6
𝑡^∗=1+((𝑘^2+√1+𝑘^4)/2)	Iter	3	3	3	3	3.5	4	4	4.5