## Abstract

We revisit and investigate the application of an infinite mapping layer in the context of different physical fields. This layer remaps the infinite physical domain to a finite extension covering the boundary of the computational domain. Thus, infinite domain problems are solved efficiently by this advanced finite element method. Compared to infinite elements, this method has major practical advantages since it uses standard basis functions. However, the solution at the outer boundary of the infinite layer must be bounded. In principle, this method can be applied to arbitrarily shaped mapping layers.

The presented method is verified against three physical field problems and their analytic solution. Firstly, the computation of the electrostatic potential in an unbounded region is investigated. Secondly, a benchmark problem of mechanical engineering demonstrates the method for continuum mechanics. Finally, eigenmodes of deep water waves are solved accurately. For these three cases, we assess three different mapping functions of tangent, exponential, and rational type and comment on their suitability for different physical field problems. The method guarantees high efficiency and accuracy, as shown by the application examples.

The presented method is verified against three physical field problems and their analytic solution. Firstly, the computation of the electrostatic potential in an unbounded region is investigated. Secondly, a benchmark problem of mechanical engineering demonstrates the method for continuum mechanics. Finally, eigenmodes of deep water waves are solved accurately. For these three cases, we assess three different mapping functions of tangent, exponential, and rational type and comment on their suitability for different physical field problems. The method guarantees high efficiency and accuracy, as shown by the application examples.

Original language | English |
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Pages (from-to) | 354-367 |

Journal | Journal of Computational Physics |

Volume | 392 |

DOIs | |

Publication status | Published - 1 Sept 2019 |

## Keywords

- Finite element method
- Infinite domain
- Mechanics
- Electrostatics
- Deep water waves