Fast collocation method for a two-dimensional variable-coefficient linear nonlocal diffusion model

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 2 Performance of FCG, CG, and Gauss while \(s=3/8\)

	\(N_{x} = N_{y}\)	\(\\| \mathbf{u}_{h} - \mathbf{u} \\|_{L^{2}}\)	# of iter.	CPUs
Gauss	2⁴	2.2848 × 10⁻²		0.73 s
	2⁵	1.6317 × 10⁻²		20 s
	2⁶	9.8298 × 10⁻³		19 m 2 s
	2⁷			> 10 h
	2⁸		out of memory
		\(C_{\alpha } = 0.13\), α = 0.61
CGS	2⁴	2.2848 × 10⁻²	33	0.53 s
	2⁵	1.6317 × 10⁻²	104	8.1 s
	2⁶	9.8298 × 10⁻³	165	3 m 49 s
	2⁷			> 10 h
	2⁸		out of memory
		\(C_{\alpha } = 0.13\), α = 0.61
FCGS	2⁴	2.2848 × 10⁻²	32	0.1 s
	2⁵	1.6317 × 10⁻²	104	1 s
	2⁶	9.8298 × 10⁻³	165	15.82 s
	2⁷	4.9156 × 10⁻³	303	1 m 19 s
	2⁸	2.2000 × 10⁻³	625	11 m 59 s
		\(C_{\alpha } = 0.28\), α = 0.85