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.

翻译：我们考虑的是一组数学模型,描述通过界面互动的多物理现象。在这样的界面上,字段的痕迹(大约)在两个分数操作员的加权总和范围内。我们使用一种合理的函数近似值作为这些操作员的前提条件。我们首先展示了分数计的加权总和给出的普通函数近似值的稳健性。此外,我们提出了更现实的例子,利用提议的在达西和斯托克斯方程式之间连接的先决条件技术。