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Thursday, March 16 • 4:00pm - 5:30pm
Poster: A High Order Accurate Direct Solution Technique for High Frequency Problems with Body Loads

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Differential equations with highly oscillatory arise in many areas of
science and engineering including geophysics, material science, fluid
dynamics, and medical imaging. When solutions are highly oscillatory,
classic discretization techniques suffer from dispersion and poor
conditioning, which result in accuracy issues and slow convergence for
iterative solvers. This poster presents the recently developed
Hierarchical Poincare-Steklov (HPS) method. The HPS method is a high
order discretization technique that provides accurate solutions even in
the high frequency regime. For example, a problem with 64 wavelengths
per side was solved to 8 digits of accuracy with 16 points per wavelength.
Additionally, the method comes with a direct (as opposed to iterative) solver
that processes solves with nearly linear cost with respect to the number of
discretization points, avoiding the poor performance of iterative solvers
for highly oscillatory solutions. For a test problem with more than 4
million unknowns, after precomputation, the solve takes less than 5
seconds on a modest desktop computer. Since solves are so inexpensive,
the method is ideal for problems with many right hand sides, such as occur
in most applications of interest. Numerical results will illustrate the
performance of the method for a variety of test problems.


Thursday March 16, 2017 4:00pm - 5:30pm
Exhibit Hall BRC