Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 8 The error norms and CPU (seconds) for a multigrid method with different discretized schemes for Example 3 , \(\pmb{\|e\|_{2}}\) , \(\pmb{k = 10}\)

From: Multigrid method based on transformation-free high-order scheme for solving 2D Helmholtz equation on nonuniform grids

N	CDS scheme	CPU (seconds)	Order	HOC scheme	Order
4	\(7.5620e^{-2}\)	0.060	2.01	\(6.3220e^{-4}\)	2.40
8	\(3.2228e^{-3}\)	0.074	4.55	\(8.3311e^{-5}\)	2.92
16	\(4.0644e^{-4}\)	0.088	2.98	\(3.2034e^{-6}\)	4.70
32	\(8.1510e^{-5}\)	1.03	2.31	\(8.1284e^{-7}\)	1.97
64	\(2.0389e^{-6}\)	1.80	5.32	\(7.3819e^{-8}\)	3.46
128	\(5.5090e^{-7}\)	2.90	1.43	\(6.1901e^{-8}\)	0.25

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