# A high-order multiscale finite-element method for time-domain acoustic-wave modeling

## Abstract

Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructs high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss–Lobatto–Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- The Chinese Univ. of Hong Kong (Hong Kong)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE Office of Energy Efficiency and Renewable Energy (EERE). Geothermal Technologies Office (EE-4G)

- OSTI Identifier:
- 1425765

- Report Number(s):
- LA-UR-17-28501

Journal ID: ISSN 0021-9991

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 360; Journal Issue: C; Journal ID: ISSN 0021-9991

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Earth Sciences

### Citation Formats

```
Gao, Kai, Fu, Shubin, and Chung, Eric T.
```*A high-order multiscale finite-element method for time-domain acoustic-wave modeling*. United States: N. p., 2018.
Web. doi:10.1016/j.jcp.2018.01.032.

```
Gao, Kai, Fu, Shubin, & Chung, Eric T.
```*A high-order multiscale finite-element method for time-domain acoustic-wave modeling*. United States. doi:10.1016/j.jcp.2018.01.032.

```
Gao, Kai, Fu, Shubin, and Chung, Eric T. Sun .
"A high-order multiscale finite-element method for time-domain acoustic-wave modeling". United States.
doi:10.1016/j.jcp.2018.01.032.
```

```
@article{osti_1425765,
```

title = {A high-order multiscale finite-element method for time-domain acoustic-wave modeling},

author = {Gao, Kai and Fu, Shubin and Chung, Eric T.},

abstractNote = {Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructs high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss–Lobatto–Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.},

doi = {10.1016/j.jcp.2018.01.032},

journal = {Journal of Computational Physics},

number = C,

volume = 360,

place = {United States},

year = {Sun Feb 04 00:00:00 EST 2018},

month = {Sun Feb 04 00:00:00 EST 2018}

}