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Convergence analysis of a class of massively parallel direction splitting algorithms for the NavierStokes equations in simple domains
 Mathematics of Computation
"... Abstract. We provide a convergence analysis for a new fractional timestepping technique for the incompressible NavierStokes equations based on direction splitting. This new technique is of linear complexity, unconditionally stable and convergent, and suitable for massive parallelization. 1. ..."
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Abstract. We provide a convergence analysis for a new fractional timestepping technique for the incompressible NavierStokes equations based on direction splitting. This new technique is of linear complexity, unconditionally stable and convergent, and suitable for massive parallelization. 1.
ADI SPLITTING SCHEMES FOR A FOURTHORDER NONLINEAR PARTIAL DIFFERENTIAL EQUATION FROM IMAGE PROCESSING
"... Abstract. We present directional operator splitting schemes for the numerical solution of a fourthorder, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1gradient flow of the total variation and represents a prototype of higheror ..."
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Abstract. We present directional operator splitting schemes for the numerical solution of a fourthorder, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1gradient flow of the total variation and represents a prototype of higherorder equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit timestepping provides a stable and computationally cheap numerical realisation of the equation. 1. Introduction. In
total variation image minimization problem
"... Nonlinear multilevel schemes for solving the ..."
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www.elsevier.com/locate/apnum A piecewise constant level set method for elliptic inverse problems
, 2006
"... We apply a piecewise constant level set method to elliptic inverse problems. The discontinuity of the coefficients is represented implicitly by a piecewise constant level set function, which allows to use one level set function to represent multiple phases. The inverse problem is solved using a vari ..."
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We apply a piecewise constant level set method to elliptic inverse problems. The discontinuity of the coefficients is represented implicitly by a piecewise constant level set function, which allows to use one level set function to represent multiple phases. The inverse problem is solved using a variational penalization method with the total variation regularization of the coefficients. An operator splitting scheme is used to get efficient and robust numerical schemes for solving the obtained problem. Numerical experiments show that the method can recover coefficients with rather complicated geometry of discontinuities under a moderate amount of noise in the observation data. © 2006 IMACS. Published by Elsevier B.V. All rights reserved.