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Applied Math Seminar – Hongsong Feng, University of Alabama
January 17 @ 11:00 am - 12:00 pm
Title: Augmented matched interface and boundary(AMIB) method for elliptic interface problem and a high order fast Poisson solver
Abstract: The elliptic interface problem plays an important role in fields such as electromagnetics, bimolecular electrostatics, and material science. This talk introduces augmented matched interface and boundary method that is applied to obtain second order fast solution for two-dimensional elliptic interface problem with piecewise constant coefficients. By employing auxiliary variables in a Schur complement procedure, the discrete Laplacian of the central difference can be efficiently inverted by fast Fourier transform(FFT). The total computational cost of the AMIB is about O(n^2log(n)) for the Cartesian grid with dimension n by n in 2D. This method significantly saves computational time, while second order accuracy is obtained in dealing with complicated interface. The same augmented approach is also deployed to construct a systematic high order fast Poisson solver on a rectangular domain, which can handle various boundary conditions, and achieve computational complexity of O(n^3log(n)) for 3D Poisson problem.