Computational Math Seminar: Brad Martin
Seismic wave simulation through radial basis function-derived finite differences (RBF-FD): preliminary results from a new 3rd-order numerical method.
Brad Martin
Applied Mathematics,Ìý
Date and time:Ìý
Tuesday, February 18, 2014 - 10:30am
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Grandview Conference Room, 1320 Grandview Avenue
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Numerically solving hyperbolic partial differential equations (PDEs) within domains featuring discontinuous PDE parameters is an important process in a number of scientific fields.Ìý Here, we discuss a new RBF-FD-based approach to accurately simulate elastic waves in 2D.Ìý Finite difference weights are constructed using a traditional RBF basis (continuous across interfaces) along with specially modified support polynomials (possibly kinked and even discontinuous across the interface).Ìý The combined RBF and polynomial bases are designed to enforce physically correct continuity conditions across the interface.Ìý Convergence of the method currently appears to be 3rd-order – which agrees with heuristics on how the implementation was designed – but near-future refinements may allow a straightforward extension to a higher order of accuracy (depending on stability issues).