Published:January 01, 2012
Björn Engquist, Lexing Ying, 2012. "Sweeping preconditioner for the Helmholtz equation: Hierarchical matrix representation", Numerical Modeling of Seismic Wave Propagation: Gridded Two-way Wave-equation Methods, Johan O. A. Robertsson, Joakim O. Blanch, Kurt Nihei, Jeroen Tromp
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The paper introduces the sweeping preconditioner, which is highly efficient for iterative solutions of the variable-coefficient Helmholtz equation including veryhigh-frequency problems. The first central idea of this novel approach is to construct an approximate factorization of the discretized Helmholtz equation by sweeping the domain layer by layer, starting from an absorbing layer or boundary condition. Given this specific order of factorization, the second central idea is to represent the intermediate matrices in the hierarchical matrix framework. In two dimensions, both the construction and the application of the preconditioners are of linear complexity. The generalized minimal residual method (GMRES) solver...
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Numerical Modeling of Seismic Wave Propagation: Gridded Two-way Wave-equation Methods
“Modeling of seismic wave propagation is a core component in almost every aspect of exploration seismology, ranging from survey design methods to imaging and inversion algorithms. The last time SEG published a reprint volume on numerical modeling was in 1990. Since then, the last two decades has seen a step change in the application and use of Â"full wave equationÂ" modeling methods enabled by the tremendous increase in available computational power. Full waveform inversion, reverse time migration and 3D elastic finitedifference synthetic data generation are examples of modeling applications that are currently having a fundamental impact on our business. In Numerical Modeling of Seismic Wave Propagation: Gridded Two-way Wave-equation Methods, readers will find many of the wellknown and referenced papers from the exploration seismic community as well as some of the key papers that have impacted other fields of seismology. Because the modeling literature is vast, we have limited the scope of the reprint volume to papers over the last two decades on modeling methods based on the full wave equation. The reprint volume will be of particular interest to researchers and practitioners interested in modeling methods and their applications. The searchable CD includes the 114-page book of abstracts and the full papers.”