论文标题
多物理问题的理性近似预处理
Rational approximation preconditioners for multiphysics problems
论文作者
论文摘要
我们考虑了描述通过界面相互作用的多物理现象的一类数学模型。在这样的界面上，磁场的痕迹（大约）位于两个分数差分运算符的加权总和的范围内。我们对此类操作员使用有理函数近似。我们首先证明了由分数指数加权总和给出的普通函数的近似值的鲁棒性。此外，我们提出了利用Darcy和Stokes方程之间界面耦合中提出的预处理技术的更现实的例子。
We consider a class of mathematical models describing multiphysics phenomena interacting through interfaces. On such interfaces, the traces of the fields lie (approximately) in the range of a weighted sum of two fractional differential operators. We use a rational function approximation to precondition such operators. We first demonstrate the robustness of the approximation for ordinary functions given by weighted sums of fractional exponents. Additionally, we present more realistic examples utilizing the proposed preconditioning techniques in interface coupling between Darcy and Stokes equations.
