The Extrinsic Enriched Finite Element Method with Appropriate Enrichment Functions for the Helmholtz Equation

The traditional finite element method (FEM) could only provide acceptable numerical solutions for the Helmholtz equation in relatively small wave number range due to dispersion errors. For large numbers, corresponding FE are never adequately reliable. With aim enhance performance of FEM tackling equation, this work an extrinsic enriched (EFEM) is proposed reduce inherent errors standard solutions. In EFEM, linear approximation space extrinsically by using polynomial and trigonometric functions. construction realized based on partition unity concept highly oscillating features numbers can be effectively captured employed specially-designed enrichment A typical examples considered examine ability EFEM control error solving problems. From obtained results, it found that behaves much better than suppressing effects more accurate results. addition, also possesses higher convergence rate conventional FEM. More importantly, formulation formulated quite easily without adding extra nodes. Therefore, present regarded as a competitive alternative approach dealing with high frequency ranges.