New Block Triangular Preconditioners for Saddle Point Linear Systems with Highly Singular (1,1) Blocks

Table 4

Number and time of iterations of GMRES(10) with preconditioners ℳ_𝑡 and ℳ for different drop tolerances 𝜏 , 𝑡 when ℎ=1/32. Results of preconditioner ℳ lie inside [].

𝜏	𝑡=−1	Time (−1)	𝑡=1	Time (1)	𝑡=2	Time (2)
0.01	3(30)	4.0938	9(83)	11.4688	9(89)	12.1563
	[10(93)]	[12.7344]	[11(103)]	[14.1875]	[13(128)]	[17.4219]
0.005	3(28)	3.8906	7(67)	9.1563	8(74)	10.1719
	[8(76)]	[10.4375]	[9(86)]	[11.9688]	[12(118)]	[16.1719]
0.001	3(22)	3.1719	5(44)	6.2813	5(45)	6.3438
	[6(52)]	[7.3594]	[7(65)]	[9.1719]	[11(105)]	[14.7344]
0.0001	2(18)	2.8906	3(30)	4.6875	4(32)	5.0313
	[4(39)]	[6.0000]	[6(58)]	[8.9688]	[10(94)]	[14.5000]