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Thursday, March 3 • 11:10am - 11:30am
Algorithms & Accelerators II: An Efficient High Accuracy Discretization and Direct Solution Technique for Variable Coefficient Partial Differential Equations

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The ability to efficiently and accurately solve variable coefficient partial differential equations (PDEs) is a critical for numerical simulations in seismic imaging. In this talk, we present a high-order accurate discretization technique for these challenging problems that comes complete with with an efficient and robust direct solver. The method utilizes local high order discretization gluing neighboring regions with continuum operators. The resulting sparse linear system is inherently amenable to a direct solver similar to nested dissection whose asymptotic scaling is no worse than O(N^{3/2}) precomputation where N is the number of discretization points. The cost of the applying the solver scales (at worst O(N log(N)) with a tiny constant). The result is a method that ideally suited for the ill-conditioned problems with many right hand-sides that consistently arise in the seismic imaging community. For applications where the coefficients of the PDE change locally in the geometry, such as in many inversion algorithms, the proposed method is naturally able to re-use information from the static regions making local updates extremely inexpensive. Numerical results will illustrate the performance of the proposed method.


Thursday March 3, 2016 11:10am - 11:30am
BioScience Research Collaborative Building (BRC), Room 280 & 282

Attendees (2)