Elliptic Interface Problem

Elliptic interface problems involve solving partial differential equations with discontinuous coefficients or boundary conditions across interfaces, a challenge arising in diverse fields like fluid dynamics and materials science. Current research heavily utilizes physics-informed neural networks (PINNs), often coupled with domain decomposition methods and various interface condition strategies (e.g., Robin, Dirichlet-Neumann), to achieve efficient and accurate solutions, even for complex geometries and high-contrast coefficients. These advancements improve upon traditional numerical methods by offering mesh-free approaches and enhanced scalability, particularly for problems with irregular interfaces or multiple coupled equations. The resulting improvements in computational efficiency and accuracy have significant implications for modeling complex physical phenomena across various scientific and engineering disciplines.