Smoothed Circulant Embedding with Applications to Multilevel Monte Carlo Methods for PDEs with Random Coefficients
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910740287324160 |
|---|---|
| author | Istratuca, Anastasia Teckentrup, Aretha |
| author_facet | Istratuca, Anastasia Teckentrup, Aretha |
| contents | We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a commonly used model for the unknown parameter is a random field. We make use of the circulant embedding procedure for sampling from the aforementioned coefficient. To improve the computational complexity of the MLMC estimator in the case of highly oscillatory random fields, we devise and implement a smoothing technique integrated into the circulant embedding method. This allows to choose the coarsest mesh on the first level of MLMC independently of the correlation length of the covariance function of the random field, leading to considerable savings in computational cost. We illustrate this with numerical experiments, where we see a saving of factor 5-10 in computational cost for accuracies of practical interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_13493 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Smoothed Circulant Embedding with Applications to Multilevel Monte Carlo Methods for PDEs with Random Coefficients Istratuca, Anastasia Teckentrup, Aretha Numerical Analysis We consider the computational efficiency of Monte Carlo (MC) and Multilevel Monte Carlo (MLMC) methods applied to partial differential equations with random coefficients. These arise, for example, in groundwater flow modelling, where a commonly used model for the unknown parameter is a random field. We make use of the circulant embedding procedure for sampling from the aforementioned coefficient. To improve the computational complexity of the MLMC estimator in the case of highly oscillatory random fields, we devise and implement a smoothing technique integrated into the circulant embedding method. This allows to choose the coarsest mesh on the first level of MLMC independently of the correlation length of the covariance function of the random field, leading to considerable savings in computational cost. We illustrate this with numerical experiments, where we see a saving of factor 5-10 in computational cost for accuracies of practical interest. |
| title | Smoothed Circulant Embedding with Applications to Multilevel Monte Carlo Methods for PDEs with Random Coefficients |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2306.13493 |