# Time splitting for wave equations in random media

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

- Volume: 38, Issue: 6, page 961-987
- ISSN: 0764-583X

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topBal, Guillaume, and Ryzhik, Lenya. "Time splitting for wave equations in random media." ESAIM: Mathematical Modelling and Numerical Analysis 38.6 (2010): 961-987. <http://eudml.org/doc/194251>.

@article{Bal2010,

abstract = {
Numerical simulation of high frequency waves in highly heterogeneous
media is a challenging problem. Resolving the fine structure of the
wave field typically requires extremely small time steps and spatial
meshes. We show that capturing macroscopic quantities of the wave
field, such as the wave energy density, is achievable with much
coarser discretizations. We obtain such a result using a time
splitting algorithm that solves separately and successively
propagation and scattering in the simplified regime of the parabolic
wave equation in a random medium. The mathematical theory of the
convergence and statistical properties of the algorithm is based on
the analysis of the Wigner transforms in random media. Our results
provide a step toward understanding time and space discretizations
that are needed in order for the numerical algorithm to capture the
correct macroscopic statistics of the wave energy density in a
random medium.
},

author = {Bal, Guillaume, Ryzhik, Lenya},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {High frequency waves in random media; time splitting; multiscale analysis.},

language = {eng},

month = {3},

number = {6},

pages = {961-987},

publisher = {EDP Sciences},

title = {Time splitting for wave equations in random media},

url = {http://eudml.org/doc/194251},

volume = {38},

year = {2010},

}

TY - JOUR

AU - Bal, Guillaume

AU - Ryzhik, Lenya

TI - Time splitting for wave equations in random media

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2010/3//

PB - EDP Sciences

VL - 38

IS - 6

SP - 961

EP - 987

AB -
Numerical simulation of high frequency waves in highly heterogeneous
media is a challenging problem. Resolving the fine structure of the
wave field typically requires extremely small time steps and spatial
meshes. We show that capturing macroscopic quantities of the wave
field, such as the wave energy density, is achievable with much
coarser discretizations. We obtain such a result using a time
splitting algorithm that solves separately and successively
propagation and scattering in the simplified regime of the parabolic
wave equation in a random medium. The mathematical theory of the
convergence and statistical properties of the algorithm is based on
the analysis of the Wigner transforms in random media. Our results
provide a step toward understanding time and space discretizations
that are needed in order for the numerical algorithm to capture the
correct macroscopic statistics of the wave energy density in a
random medium.

LA - eng

KW - High frequency waves in random media; time splitting; multiscale analysis.

UR - http://eudml.org/doc/194251

ER -

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