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13 papers · 2 filters
Zernike Polynomials: Evaluation, Quadrature, and Interpolation
Philip Greengard, Kirill Serkh
Zernike polynomials are a basis of orthogonal polynomials on the unit disk that are a natural basis for representing smooth functions. They arise in a number of applications includ…
On the accurate evaluation of unsteady Stokes layer potentials in moving two-dimensional geometries
Leslie Greengard, Shidong Jiang, Jun Wang
Two fundamental difficulties are encountered in the numerical evaluation of time-dependent layer potentials. One is the quadratic cost of history dependence, which has been success…
Seismic Inversion and the Data Normalization for Optimal Transport
Björn Engquist, Yunan Yang
Full waveform inversion (FWI) has recently become a favorite technique for the inverse problem of finding properties in the earth from measurements of vibrations of seismic waves o…
A new mixed potential representation for the equations of unsteady, incompressible flow
Leslie Greengard, Shidong Jiang
We present a new integral representation for the unsteady, incompressible Stokes or Navier-Stokes equations, based on a linear combination of heat and harmonic potentials. For velo…
A comparative study of structural similarity and regularization for joint inverse problems governed by PDEs
Benjamin Crestel, Georg Stadler, Omar Ghattas
Joint inversion refers to the simultaneous inference of multiple parameter fields from observations of systems governed by single or multiple forward models. In many cases these pa…
Seismic Imaging and Optimal Transport
Björn Engquist, Yunan Yang
Seismology has been an active science for a long time. It changed character about 50 years ago when the earth's vibrations could be measured on the surface more accurately and more…