论文标题
线性化杂交不连续的Galerkin方法：线性缩放运算符
Linearizing the hybridizable discontinuous Galerkin method: A linearly scaling operator
论文作者
论文摘要
本文提出了一种无基质剩余评估技术，该技术针对可杂交的不连续的盖尔金方法，需要许多操作仅按照自由度的数量进行线性缩放。该方法是由于在立方体笛卡尔元素上应用张量产物碱的应用，罚款参数的特定选择以及快速对角线化技术。结合线性缩放，面对面的预处理，可以实现连接梯度方法的线性缩放时间。这允许在一个CPU核心上以每未知数为1 $μs$的解决方案 - 通常与低阶方法相关的数字。
This paper proposes a matrix-free residual evaluation technique for the hybridizable discontinuous Galerkin method requiring a number of operations scaling only linearly with the number of degrees of freedom. The method results from application of tensor-product bases on cuboidal Cartesian elements, a specific choice for the penalty parameter, and the fast diagonalization technique. In combination with a linearly scaling, face-wise preconditioner, a linearly scaling iteration time for a conjugate gradient method is attained. This allows for solutions in 1 $μs$ per unknown on one CPU core - a number typically associated with low-order methods.
