Journal of Applied Mathematics / 2012 / Article / Tab 8

Research Article

Adaptive Double-Diffusion Model and Comparison to a Highly Heterogeneous Micro-Model

Table 8

Cost of one-grid versus two-grid discretization in a simulation with 1,000 time steps.

One-grid with β„Ž 1 = β„Ž 2 = 1 / 8 0
Matrix Cost (seconds)

𝑆 1 , β„Ž 1 + 𝑀 1 , β„Ž 1 3.6547
𝐡 o n e - g r i d 0.0123
Solve π•Š o n e - g r i d 1,000 times0.2761 Γ— 1,000

Total279.7670

Two-grid with β„Ž 1 = 1 / 8 0 , β„Ž 2 = 1 / 2 0
Matrix Cost (seconds)

𝑆 1 , β„Ž 1 + 𝑀 1 , β„Ž 1 3.6547
𝑀 2 , β„Ž 2 0.0438
𝕀 β„Ž 1 , β„Ž 2 0.2121
𝐡 t w o - g r i d 0.0063
Solve π•Š t w o - g r i d 1,000 times 0.1030 Γ— 1,000

Total106.9169