Numerical analysis of a time-stepping method for the Westervelt equation with time-fractional damping
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2022
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866909077565603840 |
|---|---|
| author | Baker, Katherine Banjai, Lehel Ptashnyk, Mariya |
| author_facet | Baker, Katherine Banjai, Lehel Ptashnyk, Mariya |
| contents | We develop a numerical method for the Westervelt equation, an important equation in nonlinear acoustics, in the form where the attenuation is represented by a class of non-local in time operators. A semi-discretisation in time based on the trapezoidal rule and A-stable convolution quadrature is stated and analysed. Existence and regularity analysis of the continuous equations informs the stability and error analysis of the semi-discrete system. The error analysis includes the consideration of the singularity at $t = 0$ which is addressed by the use of a correction in the numerical scheme. Extensive numerical experiments confirm the theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_16349 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Numerical analysis of a time-stepping method for the Westervelt equation with time-fractional damping Baker, Katherine Banjai, Lehel Ptashnyk, Mariya Numerical Analysis Analysis of PDEs 35L77, 65M06, 65M15, 35R11 We develop a numerical method for the Westervelt equation, an important equation in nonlinear acoustics, in the form where the attenuation is represented by a class of non-local in time operators. A semi-discretisation in time based on the trapezoidal rule and A-stable convolution quadrature is stated and analysed. Existence and regularity analysis of the continuous equations informs the stability and error analysis of the semi-discrete system. The error analysis includes the consideration of the singularity at $t = 0$ which is addressed by the use of a correction in the numerical scheme. Extensive numerical experiments confirm the theory. |
| title | Numerical analysis of a time-stepping method for the Westervelt equation with time-fractional damping |
| topic | Numerical Analysis Analysis of PDEs 35L77, 65M06, 65M15, 35R11 |
| url | https://arxiv.org/abs/2210.16349 |