Preconditioned Krylov Subspace Methods for Sixth Order Compact Approximations of the Helmholtz Equation

Table 1

3D Dirichlet problem eigenvalue bounds (different 𝑘²).

	𝑘=10	𝑘=20	𝑘=30	𝑘=40	𝑘=50
ℎ=1/64	−0.015∣0.49	−1.22∣0.49	−1.02∣0.88	−34.7∣180	−10.2∣55.0
ℎ=1/128	−0.0038∣0.49	−0.158∣0.49	−0.140∣0.64	−2.81∣0.90	−2.21∣1.74
ℎ=1/256	−0.00094∣0.49	−0.035∣0.49	−0.031∣0.49	−0.22∣0.69	−11.7∣0.56
ℎ=1/512	−0.00023∣0.49	−0.009∣0.49	−0.008∣0.49	−0.048∣0.49	−0.298∣0.49
𝛿0	8.00	4.00	1.80	1.12	2.9
ℎ1	1/64	1/128	1/256	1/256	1/512