Book review: Efficient Solvers for Incompressible Flow Problems

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Book review: Computational Partial Differential Equations

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Threshold incomplete factorization constraint preconditioners for saddle-point matrices

This paper presents a drop-threshold incomplete LD\u3csup\u3e-1\u3c/sup\u3eL\u3csup\u3eT\u3c/sup\u3e (δ) factorization constraint preconditioner for saddle-point systems using a threshold parameter δ. A transformed saddle-point matrix is partitioned into a block structure with blocks of order 1 and 2 constituting ‘a priori pivots’. Based on these pivots an incomplete LD\u3csup\u3e-1\u3c/sup\u3eL\u3csup\u3eT\u3c/sup\u3e (δ) factorization constraint preconditioner is computed that approaches an exact form as δ approaches zero. We prove that both the exact and incomplete factorizations exist such that the entries of the constraint block remain unaltered in the triangular factors. Numerical results are presented for validation

Orientation identification of the power spectrum

The image Fourier transform is widely used for defocus and astigmatism correction in electron microscopy. The shape of a power spectrum (the square of a modulus of image Fourier transform) is directly related to the three microscope’s controls, namely defocus and two-fold (two-parameter) astigmatism. In this paper the new method for power spectrum orientation identification is proposed. The method is based on the three measures which are related to the microscope’s controls. The measures are derived from the mathematical moments of the power spectrum. The method is tested with the help of a Gaussian benchmark, as well as with the scanning electron microscopy experimental images. The method can be used as an assisting tool for increasing the capabilities of defocus and astigmatism correction a of non-experienced scanning electron microscopy user, as well as a basis for automated application

A novel Krylov method for model order reduction of quadratic bilinear systems

\u3cp\u3eA novel Krylov subspace method is proposed to substantially reduce the computational complexity of the special class of quadratic bilinear dynamical systems. Based on the first two generalized transfer functions of the system, a Petrov-Galerkin projection scheme is applied. It is shown that such a projection amounts to interpolating the transfer functions at specific points which, in fact, is equivalent to constructing the corresponding Krylov subspace. For single-input single-output systems, the relevant Krylov subspace can be readily constructed for the interpolation points. For multi-input multi-output systems, also user-specified directional information is required so that a tangential interpolation can be determined. The method is demonstrated by numerical examples.\u3c/p\u3

Orientation identification of the power spectrum

\u3cp\u3eThe image Fourier transform is widely used for defocus and astigmatism correction in electron microscopy. The shape of a power spectrum (the square of a modulus of image Fourier transform) is directly related to the three microscope controls, namely, defocus and twofold (two-parameter) astigmatism. We propose a new method for power-spectrum orientation identification. The method is based on the three measures that are related to the microscope's controls. The measures are derived from the mathematical moments of the power spectrum and is tested with the help of a Gaussian benchmark, as well as with the scanning electron microscopy experimental images. The method can be used as an assisting tool for increasing the capabilities of defocus and astigmatism correction a of nonexperienced scanning electron microscopy user, as well as a basis for automated application.\u3c/p\u3