CALCLENS: Weak Lensing Simulations for Large-area Sky Surveys and
  Second-order Effects in Cosmic Shear Power Spectra
  I present a new algorithm, CALCLENS, for efficiently computing weak
gravitational lensing shear signals from large N-body light cone simulations
over a curved sky. This new algorithm properly accounts for the sky curvature
and boundary conditions, is able to produce redshift-dependent shear signals
including corrections to the Born approximation by using multiple-plane ray
tracing, and properly computes the lensed images of source galaxies in the
light cone. The key feature of this algorithm is a new, computationally
efficient Poisson solver for the sphere that combines spherical harmonic
transform and multgrid methods. As a result, large areas of sky (~10, 000
square degrees) can be ray traced efficiently at high-resolution using only a
few hundred cores on widely available machines. Using this new algorithm and
curved-sky calculations that only use a slower but more accurate spherical
harmonic transform Poisson solver, I study the shear B-mode and rotation mode
power spectra. Employing full-sky E/B-mode decompositions, I confirm that the
shear B-mode and rotation mode power spectra are equal at high accuracy (~1%),
as expected from perturbation theory up to second order. Coupled with realistic
galaxy populations placed in large N-body light cone simulations, this new
algorithm is ideally suited for the construction of synthetic weak lensing
shear catalogs to be used to test for systematic effects in data analysis
procedures for upcoming large-area sky surveys. The implementation presented in
this work, written in C and employing widely available software libraries to
maintain portability, is publicly available at
http://code.google.com/p/calclens.
