## Abstract

This paper presents a framework for implementing a novel Perfectly

Matching Layer and Infinite Element (PML+IE) combination boundary

condition for unbounded elastic wave problems in the time domain. To

achieve this, traditional hexahedral finite elements are used to model

wave propagation in the inner domain and infinite element test functions

are implemented in the exterior domain. Two alternative

implementations of the PML formulation are studied: the case with

constant stretching in all three dimensions and the case with spatially

dependent stretching along a single direction. The absorbing ability of

the PML+IE formulation is demonstrated by the favourable comparison

with the reflection coefficient for a plane wave incident on the boundary

achieved using a finite element only approach where stress free

boundary conditions are implemented at the domain edge. Values for the

PML stretching function parameters are selected based on the

minimisation of the reflected wave amplitude and it is shown that the

same reduction in reflection amplitude can be achieved using the PML+IE

approach with approximately half of the number of elements required in

the finite element only approach.

Matching Layer and Infinite Element (PML+IE) combination boundary

condition for unbounded elastic wave problems in the time domain. To

achieve this, traditional hexahedral finite elements are used to model

wave propagation in the inner domain and infinite element test functions

are implemented in the exterior domain. Two alternative

implementations of the PML formulation are studied: the case with

constant stretching in all three dimensions and the case with spatially

dependent stretching along a single direction. The absorbing ability of

the PML+IE formulation is demonstrated by the favourable comparison

with the reflection coefficient for a plane wave incident on the boundary

achieved using a finite element only approach where stress free

boundary conditions are implemented at the domain edge. Values for the

PML stretching function parameters are selected based on the

minimisation of the reflected wave amplitude and it is shown that the

same reduction in reflection amplitude can be achieved using the PML+IE

approach with approximately half of the number of elements required in

the finite element only approach.

Original language | English |
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Journal | mathematics and mechanics of solids |

Publication status | Accepted/In press - 2 Aug 2021 |

## Keywords

- Finite elements
- Infinite elements
- Perfectly matching layer
- elastic waves