Implementing EFG Method with MATLAB: Code Development and Numerical Analysis

In this article, we provide an in-depth exploration of programming EFG code using MATLAB. The Extended Finite Element Method (EFG) represents an advanced numerical computation technique extensively applied to solve various engineering and physical problems. Through MATLAB implementation, we can streamline the development and execution of EFG code with greater efficiency. The programming approach typically involves constructing shape functions using moving least squares approximation, implementing numerical integration schemes, and handling enriched degrees of freedom for crack propagation simulations. We will demonstrate key MATLAB functions including mesh generation routines, matrix assembly operations, and solver implementations for handling discontinuous phenomena. Additionally, we introduce fundamental MATLAB syntax and programming techniques, such as vectorization for performance optimization and object-oriented programming for code modularity, to help beginners better master this powerful tool and achieve improved results in practical applications. The implementation covers essential algorithms including node enrichment strategies and visibility criteria for handling material interfaces.