一種求解二維熱傳導方程的高效算法——ETF-FDS-MG方法

An Efficient Algorithm for Two-Dimension Heat-conduction Equation ETF-FDS-MG

摘要: 針對二維熱傳導問題,提出了時間為三階、空間為二階的無條件穩定的ETF-FDS-MG算法(Extended Trapezoidal Formula Finite Difference Scheme Multigrid),分析了其精度和穩定性,證明了其收斂性.數值分析實例說明ETF-FDS-MG算法的計算效率優于前人的FE-MG(有限元-多重網格)算法.

Abstract: An efficient algorithm is devised and analyzed for Two-Dimension Heat-conduction equation. It is proved that the ETF-FDS-MG(Extended Trapezoidal Formula Finite Difference Scheme Multigrid) method is third-order in time, two-order in space, unconditionally stable and high order convergent. Numerical example confirms the ETF-FDS-MG method is superior to the FE-MG(Finite Element Multigrid) method.