A New Numerical Algorithm for Thermoacoustic and Photoacoustic Tomography with Variable Sound Speed. (arXiv:1101.3729v1 [math.NA])

A New Numerical Algorithm for Thermoacoustic and Photoacoustic Tomography with Variable Sound Speed. (arXiv:1101.3729v1 [math.NA]): "

We present a new algorithm for reconstructing an unknown source in
Thermoacoustic and Photoacoustic Tomography based on the recent advances in
understanding the theoretical nature of the problem. We work with variable
sound speeds that might be also discontinuous across some surface. The latter
problem arises in brain imaging. The new algorithm is based on an explicit
formula in the form of a Neumann series. We present numerical examples with
non-trapping, trapping and piecewise smooth speeds, as well as examples with
data on a part of the boundary. These numerical examples demonstrate the robust
performance of the new algorithm.

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A posteriori error estimators suitable for moving finite element methods under anisotropic meshes. (arXiv:1101.3635v1 [math.NA])

A posteriori error estimators suitable for moving finite element methods under anisotropic meshes. (arXiv:1101.3635v1 [math.NA]): "

In this paper, we give a new type of a posteriori error estimators suitable
for moving finite element methods under anisotropic meshes for general
second-order elliptic problems. The computation of estimators is simple once
corresponding Hessian matrix is recovered. Wonderful efficiency indices are
shown in numerical experiments.

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Convergence Analysis of a Class of Massively Parallel Direction Splitting Algorithms for the Navier-Stokes Equations. (arXiv:1101.3587v1 [math.NA])

Convergence Analysis of a Class of Massively Parallel Direction Splitting Algorithms for the Navier-Stokes Equations. (arXiv:1101.3587v1 [math.NA]): "

We provide a convergence analysis for a new fractional time-stepping
technique for the incompressible Navier-Stokes equations based on direction
splitting. This new technique is of linear complexity, unconditionally stable
and convergent, and suitable for massive parallelization.

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