Boundary integral equations for elliptic systems

Monday, August 2, 2010 - 1:30pm - 2:00pm
Keller 3-180
John Strain (University of California, Berkeley)
We present locally-corrected spectral boundary integral
methods for accurate discretization and fast solution
of linear elliptic systems of PDEs. Arbitrary elliptic
systems are transformed to overdetermined first-order form,
and a boundary integral equation is derived. Ewald
summation separates the boundary integral equation into a
low-rank system with regular spectral structure, followed
by a simple local correction formula. Geometric nonuniform
fast Fourier transforms produce accurate Fourier coefficients
of piecewise-polynomial data on a d-dimensional simplicial
tessellation in RD, for arbitrary dimensions d and D.