The infinite element method is a

numerical method In numerical analysis, a numerical method is a mathematical tool designed to solve numerical problems. The implementation of a numerical method with an appropriate convergence check in a programming language is called a numerical algorithm. Mathem ...

for solving problems of engineering and

mathematical physics Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...

. It is a modification of

finite element method The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat ...

. The method divides the domain concerned into sections of infinite length. In contrast with a finite element which is approximated by polynomial expressions on a finite support, the unbounded length of the infinite element is fitted with functions allowing the evaluation of the field at the asymptote. The number of functions and points of interpolations define the accuracy of the element in the infinite direction. The method is commonly used to solve acoustic problems and allows to respect the Sommerfeld condition of non-return of the acoustic waves and the diffusion of the pressure waves in the far field.

References

{{Numerical PDE Continuum mechanics Finite element method Numerical differential equations Partial differential equations Structural analysis