1,757 research outputs found
On surface completion and image inpainting by biharmonic functions: Numerical aspects
Numerical experiments with smooth surface extension and image inpainting
using harmonic and biharmonic functions are carried out. The boundary data used
for constructing biharmonic functions are the values of the Laplacian and
normal derivatives of the functions on the boundary. Finite difference schemes
for solving these harmonic functions are discussed in detail.Comment: Revised 21 July, 2017. Revised 12 January, 2018. To appear in
International Journal of Mathematics and Mathematical Science
Fast Ewald summation for free-space Stokes potentials
We present a spectrally accurate method for the rapid evaluation of
free-space Stokes potentials, i.e. sums involving a large number of free space
Green's functions. We consider sums involving stokeslets, stresslets and
rotlets that appear in boundary integral methods and potential methods for
solving Stokes equations. The method combines the framework of the Spectral
Ewald method for periodic problems, with a very recent approach to solving the
free-space harmonic and biharmonic equations using fast Fourier transforms
(FFTs) on a uniform grid. Convolution with a truncated Gaussian function is
used to place point sources on a grid. With precomputation of a scalar grid
quantity that does not depend on these sources, the amount of oversampling of
the grids with Gaussians can be kept at a factor of two, the minimum for
aperiodic convolutions by FFTs. The resulting algorithm has a computational
complexity of O(N log N) for problems with N sources and targets. Comparison is
made with a fast multipole method (FMM) to show that the performance of the new
method is competitive.Comment: 35 pages, 15 figure
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