论文标题
分形界面问题的数值均质化
Numerical Homogenization of Fractal Interface Problems
论文作者
论文摘要
我们考虑了一类受到地球科学相关的机械接触问题启发的分形椭圆界面问题的数值均质化。一个特定的特征是解决方案空间取决于实际的分形几何形状。我们的主要结果涉及具有适当稳定性和近似特性的投影操作员的构建。然后，此类预测的存在允许从局部正交分解（LOD）和连续的子空间校正来应用现有概念，以构建对此类问题的首次多尺度离散和具有与规模无关的收敛行为的迭代代数求解器。
We consider the numerical homogenization of a class of fractal elliptic interface problems inspired by related mechanical contact problems from the geosciences. A particular feature is that the solution space depends on the actual fractal geometry. Our main results concern the construction of projection operators with suitable stability and approximation properties. The existence of such projections then allows for the application of existing concepts from localized orthogonal decomposition (LOD) and successive subspace correction to construct first multiscale discretizations and iterative algebraic solvers with scale-independent convergence behavior for this class of problems.
