期刊
ADVANCES IN DATA SCIENCE AND ADAPTIVE ANALYSIS
卷 3, 期 1-2, 页码 251-268出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S1793536911000842
关键词
Heterogeneous media; energy conserving; discontinuous multiscale finite element method
资金
- King Abdullah University of Science and Technology (KAUST) [KUS-C1-016-04]
- NSF [724704, 0811180, 0934837]
- DOE
- US Department of Energy [DE-FG03-00ER15034]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0934837] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0811180] Funding Source: National Science Foundation
Seismic data are routinely used to infer in situ properties of earth materials on many scales, ranging from global studies to investigations of surficial geological formations. While inversion and imaging algorithms utilizing these data have improved steadily, there are remaining challenges that make detailed measurements of the properties of some geologic materials very difficult. For example, the determination of the concentration and orientation of fracture systems is prohibitively expensive to simulate on the fine grid and, thus, some type of coarse-grid simulations are needed. In this paper, we describe a new multiscale finite element algorithm for simulating seismic wave propagation in heterogeneous media. This method solves the wave equation on a coarse grid using multiscale basis functions and a global coupling mechanism to relate information between fine and coarse grids. Using a mixed formulation of the wave equation and staggered discontinuous basis functions, the proposed multiscale methods have the following properties. The total wave energy is conserved. Mass matrix is diagonal on a coarse grid and explicit energy-preserving time discretization does not require solving a linear system at each time step. Multiscale basis functions can accurately capture the subgrid variations of the solution and the time stepping is performed on a coarse grid. We discuss various subgrid capturing mechanisms and present some preliminary numerical results.
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