A meshless method based on the generalized finite difference method for three-dimensional elliptic interface problems

This article presents a meshless method to solve three-dimensional elliptic interface problem. The method is based on the generalized finite difference method, which expresses the derivatives of unknown variables by linear combinations of nearby function values. The proposed method turns the interface problem into some boundary value sub-problems coupled by the interface conditions. This conversion leads to an important feature, that is, the proposed method is not sensitive to the jump coefficients or the interface's geometry. It can handle different complex interfaces by only changing the level set function of the interface in the process. Several numerical examples with sufficient complexity verify the accuracy and stability of the method. For some given examples, the method is more accurate than the classical immersed finite element method.

Automated summary

This article presents a meshless method based on the generalized finite difference method to solve three-dimensional elliptic interface problem. The method converts the interface problem into sub-problems coupled by interface conditions and is not sensitive to jump coefficients or interface geometry. It can handle different complex interfaces by changing the level set function of the interface. Numerical examples verify the accuracy and stability of the method, showing that it can be more accurate than the classical immersed finite element method.