Interface problems with discontinuous coefficients arise in numerous real-world applications, such as composite materials, fluid mechanics, and nuclear waste disposal. In this talk, we will discuss sixth-order finite difference methods (FDMs) for the Poisson interface problem with singular sources, sixth-order hybrid FDMs with the M-matrix property for the elliptic cross-interface problem, sixth-order hybrid FDMs with the M-matrix property for the elliptic interface problem with discontinuous variable coefficients, and the sixth-order FDMs for the Helmholtz interface problem with the reduced pollution effect. We then explore a derivative-orthogonal wavelet multiscale method, which ensures bounded condition numbers, for interface problems with high-frequency oscillations. To highlight the significance of finite difference methods in comparison to finite element methods, we present the distinct numerical solutions for elliptic cross-interface problems with high-frequency and high-contrast coefficients using finite element and finite difference methods. Finally, we will discuss the advantages of using high-order techniques of FDMs for solving various PDEs in future research.

Zoom Link: https://kocun.zoom.us/j/98734123181

Meeting ID: 987 3412 3181

Passcode: 611077