论文标题
用于求解线性抛物线进化方程的平行算法
A parallel algorithm for solving linear parabolic evolution equations
论文作者
论文摘要
我们提出了一种算法，用于解决线性抛物线进化方程与空间中的对称差分运算符的线性抛物线进化方程的解决方案。在早期工作的基础上，我们将这种离散化重新铸造为Schur填充方程，该方程是对手头方程弱解的准最佳近似。选择张量产品离散化，我们到达了一个非常简单的线性系统。在空间中使用小波和标准有限元元素，我们在单个处理器上的线性复杂性中求解了所得系统，当在时空和时间平行时，在单个处理器上以及在聚类复杂性上求解了。我们通过大规模平行计算来补充这些理论发现，显示了该方法的有效性。
We present an algorithm for the solution of a simultaneous space-time discretization of linear parabolic evolution equations with a symmetric differential operator in space. Building on earlier work, we recast this discretization into a Schur-complement equation whose solution is a quasi-optimal approximation to the weak solution of the equation at hand. Choosing a tensor-product discretization, we arrive at a remarkably simple linear system. Using wavelets in time and standard finite elements in space, we solve the resulting system in linear complexity on a single processor, and in polylogarithmic complexity when parallelized in both space and time. We complement these theoretical findings with large-scale parallel computations showing the effectiveness of the method.
