# 2D wave polynomials as base functions in modified FEM

• Artur Maciąg Kielce University of Technology
• Beata Maciejewska Kielce University of Technology
• Małgorzata Sokała Kielce University of Technology

### Abstract

The paper presents solutions of a two-dimensional wave equation by using Trefftz functions. Two ways of obtaining different forms of these functions are shown. The first one is based on a generating function for the wave equation and leads to recurrent formulas for functions and their derivatives. The second one is based on a Taylor series expansion and additionally uses the inverse Laplace operator. Obtained wave functions can be used to solve the wave equation in the whole considered domain or can be used as base functions in FEM. For solving the problem three kinds of modified FEM are used: nodeless, continuous and discontinuous FEM. In order to compare the results obtained with the use of the aforementioned methods, a problem of membrane vibrations has been considered.

### Keywords

Trefftz functions, wave functions, inverse operations, FEM,

### References

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Published
Jul 20, 2022
How to Cite
MACIĄG, Artur; MACIEJEWSKA, Beata; SOKAŁA, Małgorzata. 2D wave polynomials as base functions in modified FEM. Computer Assisted Methods in Engineering and Science, [S.l.], v. 15, n. 3-4, p. 265-278, july 2022. ISSN 2956-5839. Available at: <https://cames.ippt.pan.pl/index.php/cames/article/view/735>. Date accessed: 14 sep. 2024.
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