# An FEM-MLMC algorithm for a moving shutter diffraction in time stochastic model

## Abstract

We consider a moving shutter and non-deterministic generalization of the diffraction in time model introduced by Moshinsky several decades ago to study a class of quantum transients. We first develop a moving-mesh finite element method (FEM) to simulate the determisitic version of the model. We then apply the FEM and multilevel Monte Carlo (MLMC) algorithm to the stochastic moving-domain model for simulation of approximate statistical moments of the density profile of the stochastic transients.

- Authors:

- Publication Date:

- Research Org.:
- National Renewable Energy Lab. (NREL), Golden, CO (United States)

- Sponsoring Org.:
- USDOE Office of Energy Efficiency and Renewable Energy (EERE)

- Contributing Org.:
- ,Department of Applied Mathematics & Statistics, Colorado School of Mines, Golden, CO 80401, USA; ,National Renewable Energy Laboratory, Golden, CO 80401, USA

- OSTI Identifier:
- 1483301

- Report Number(s):
- NREL/JA-2C00-72812

Journal ID: ISSN 1553-524X

- DOE Contract Number:
- AC36-08GO28308

- Resource Type:
- Journal Article

- Journal Name:
- Discrete & Continuous Dynamical Systems - B

- Additional Journal Information:
- Journal Volume: 24; Journal Issue: 1; Journal ID: ISSN 1553-524X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; diffraction in time; moving-mesh; finite element method; multilevel Monte Carlo; Monte Carlo

### Citation Formats

```
Ganesh, Mahadevan, C. Reyes, Brandon, and Purkayastha, Avi.
```*An FEM-MLMC algorithm for a moving shutter diffraction in time stochastic model*. United States: N. p., 2019.
Web. doi:10.3934/dcdsb.2018107.

```
Ganesh, Mahadevan, C. Reyes, Brandon, & Purkayastha, Avi.
```*An FEM-MLMC algorithm for a moving shutter diffraction in time stochastic model*. United States. doi:10.3934/dcdsb.2018107.

```
Ganesh, Mahadevan, C. Reyes, Brandon, and Purkayastha, Avi. Tue .
"An FEM-MLMC algorithm for a moving shutter diffraction in time stochastic model". United States. doi:10.3934/dcdsb.2018107.
```

```
@article{osti_1483301,
```

title = {An FEM-MLMC algorithm for a moving shutter diffraction in time stochastic model},

author = {Ganesh, Mahadevan and C. Reyes, Brandon and Purkayastha, Avi},

abstractNote = {We consider a moving shutter and non-deterministic generalization of the diffraction in time model introduced by Moshinsky several decades ago to study a class of quantum transients. We first develop a moving-mesh finite element method (FEM) to simulate the determisitic version of the model. We then apply the FEM and multilevel Monte Carlo (MLMC) algorithm to the stochastic moving-domain model for simulation of approximate statistical moments of the density profile of the stochastic transients.},

doi = {10.3934/dcdsb.2018107},

journal = {Discrete & Continuous Dynamical Systems - B},

issn = {1553-524X},

number = 1,

volume = 24,

place = {United States},

year = {2019},

month = {1}

}

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