176 research outputs found
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Mini-Workshop: Efficient and Robust Approximation of the Helmholtz Equation
The accurate and efficient treatment of wave propogation phenomena is still a challenging problem. A prototypical equation is the Helmholtz equation at high wavenumbers. For this equation, Babuška & Sauter showed in 2000 in their seminal SIAM Review paper that standard discretizations must fail in the sense that the ratio of true error and best approximation error has to grow with the frequency. This has spurred the development of alternative, non-standard discretization techniques. This workshop focused on evaluating and comparing these different approaches also with a view to their applicability to more general wave propagation problems
Time-stepping beyond CFL: a locally one-dimensional scheme for acoustic wave propagation
In this abstract, we present a case study in the application of a time-stepping method, unconstrained by the CFL condition, for computational acoustic wave propagation in the context of full waveform inversion. The numerical scheme is a locally one-dimensional (LOD) variant of alternating dimension implicit (ADI) method. The LOD method has a maximum time step that is restricted only by the Nyquist sampling rate. The advantage over traditional explicit time-stepping methods occurs in the presence of high contrast media, low frequencies, and steep, narrow perfectly matched layers (PML). The main technical point of the note, from a numerical analysis perspective, is that the LOD scheme is adapted to the presence of a PML. A complexity study is presented and an application to full waveform inversion is shown.National Science Foundation (U.S.); Alfred P. Sloan Foundatio
Time-stepping beyond CFL: A locally one-dimensional scheme for acoustic wave propagation
In this abstract, we present a case study in the application of a time-stepping method, unconstrained by the CFL condition, for computational acoustic wave propagation in the context of full waveform inversion. The numerical scheme is a locally one-dimensional (LOD) variant of alternating dimension implicit (ADI) method. The LOD method has a maximum time step that is restricted only by the Nyquist sampling rate. The advantage over traditional explicit time-stepping methods occurs in the presence of high contrast media, low frequencies, and steep, narrow perfectly matched layers (PML). The main technical point of the note, from a numerical analysis perspective, is that the LOD scheme is adapted to the presence of a PML. A complexity study is presented and an application to full waveform inversion is shown.TOTAL (Firm)Alfred P. Sloan FoundationNational Science Foundation (U.S.
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