热传导方程的并行与串行求解实验

Parallel and serial solution experiment of heat conduction equation

针对一维热传导方程的隐格式和六点对称格式离散形成的三对角系数矩阵,给出了具体的并行求解实验.通过应用并行计算中经典的局部消元、解耦和回代方法求解大型线性方程组,避免了计算的复杂性,并理论分析了计算量,最后通过具体的数值实验,与Gauss消去法和LU分解法进行了对比.

For the im plicit scheme of one-dimensional heat conduction equation and the tridiagonal coefficient matrix formed by six-point symmetric scheme discretization,a specific parallel solution experiment is given.By applying the classical local elimination,decoupling and backstepping methods in parallel computation to solve large-scale linear equations,the computational complexity is avoided.Moreover,the amounts of calculation are analyzed theoretically.Finally,the effect of solution within the parallel method and Gauss and LU decomposition methods is compared through concrete numerical experiment.