分形界面问题的数值均匀化
Numerical Homogenization of Fractal Interface Problems
摘要：
我们考虑一类分形椭圆界面问题的数值均匀化，其灵感来自于地球科学中相关的力学接触问题。一个特别的特点是，解决方案的空间取决于实际的分形几何。我们的主要结果涉及投影算子的建设具有适当的稳定性和逼近性能。这样的投影的存在，然后允许应用现有的概念，从本地化正交分解（LOD）和连续子空间校正构造第一多尺度离散化和迭代代数求解器与规模无关的收敛行为，这类问题。
英文摘要：
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.
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