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Your search keyword '"Knizhnerman, L."' showing total 32 results
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32 results on '"Knizhnerman, L."'

1. Krylov subspace residual and restarting for certain second order differential equations

Author

Botchev, M. A., Knizhnerman, L. A., and Schweitzer, M.

Subjects
Mathematics - Numerical Analysis, 65F60, 65M20, 65L05
Abstract

We propose algorithms for efficient time integration of large systems of oscillatory second order ordinary differential equations (ODEs) whose solution can be expressed in terms of trigonometric matrix functions. Our algorithms are based on a residual notion for second order ODEs, which allows to extend the ``residual-time restarting'' Krylov subspace framework -- which was recently introduced for exponential and $\varphi$-functions occurring in time integration of first order ODEs -- to our setting. We then show that the computational cost can be further reduced in many cases by using our restarting in the Gautschi cosine scheme. We analyze residual convergence in terms of Faber and Chebyshev series and supplement these theoretical results by numerical experiments illustrating the efficiency of the proposed methods.

Published
2022

8. A black-box rational Arnoldi variant for Cauchy-Stieltjes matrix functions

Author

Guettel, S and Knizhnerman, L

Abstract

Rational Arnoldi is a powerful method for approximating functions of large sparse matrices times a vector. The selection of asymptotically optimal parameters for this method is crucial for its fast convergence. We present and investigate a novel strategy for the automated parameter selection when the function to be approximated is of Cauchy-Stieltjes (or Markov) type, such as the matrix square root or the logarithm. The performance of this approach is demonstrated by numerical examples involving symmetric and nonsymmetric matrices. These examples suggest that our black-box method performs at least as well, and typically better, as the standard rational Arnoldi method with parameters being manually optimized for a given matrix.

Published
2016

9. BIT Numerical Mathematics: Editorial

Author

Åhlander, K., Allen, E., Aptekarev, A. I., Arioli, M., Arnold, M., Asadzadeh, M., Baglama, J., Bailly, C., Baker, C., Bartels, S., Bendali, A., Benzi, M., Berntsson, F., Breda, D., Brunner, H., SERRA CAPIZZANO, Stefano, Cash, J., Chan, R., Chandrasekaran, S., Chang, X. W., Chern, I. L., Crouzeix, M., Van Daele, M., Damhaug, A. C., Davis, T., Davydov, O., Dieci, L., Eriksson, J., Eriksson, L. E., Espelid, T., Estep, D., Fontich, E., Ford, N., Fornberg, B., Foster, L., Frank, J., Gander, W., Garća Palomares, U. M., Giraud, L., Greenbaum, A., Gripenberg, G., Gulliksson, M., Gustafsson, B., Gustafsson, N., Hairer, E., Hanke, M., Heggernes, P., Van Emden Henson, N., Hesthaven, J., Sanz, I. H., Hochbruck, M., Hochstenbach, M., Huckle, T., Kamvar, S., Kaps, P., Karlsen, K. H., Klarbring, A., Knizhnerman, L., Kopotum, K., Korotov, S., Kuijlaars, A., Kværnø, A., Langtangen, H. P., Larsson, E., Lenarduzzi, L., Lewalle, J., R. C., Li, Lin, P., Malyshev, A., Marletta, M., Mazzia, F., Mehl, C., Moore, P., Müller, B., Mørken, K., Neytcheva, M., Niederman, L., Olver, S., Ostrouchov, G., Pareschi, L., Parlett, B. N., Pralet, S., Raghavan, P., Rannacher, R., Runborg, O., Ruuth, S., Sand, J., Saunders, M., Sauter, S., Savaré, G., Shen, W. Z., Sidi, A., Spiteri, R., Steihaug, T., Stenger, F., Stoer, J., Strakoš, Z., and Tang, T.

Subjects
Computational Mathematics, Applied Mathematics, Computer Graphics and Computer-Aided Design, Software
Published
2005

25. Solution of 3D time-domain electromagnetic problems using optimal subspace projection.

Author

Zaslavsky, M., Druskin, V., and Knizhnerman, L.

Subjects
TIME-domain analysis, ELECTROMAGNETISM, DECOMPOSITION method, LAPLACE transformation, ALGORITHMS, FINITE differences, FOURIER transforms
Abstract

Time-domain problems for controlled-source electromagnetic exploration require accurate discretization of the solution for multiple spacial and temporal scales. Therefore, forward simulation using conventional computational methods becomes computationally expensive, even without accounting for induced-polarization (IP) effects. These effects create another complication caused by the presence of a convolution integral in the time-domain Maxwell system. We suggested a novel, fast, and robust algorithm to solve the 3D time-domain electromagnetic (EM) problems that can be considered as a generalization of the spectral Lanczos decomposition method. The new method also allowed us to incorporate the IP effects without significant cost increase. The discretized large-scale Maxwell system was projected onto a small subspace consisting of the-Laplace- domain solutions (the so-called parameter-dependent Kiylov subspace) for an optimally chosen set of Laplace parameters. The projected system preserved stability and passivity of the original problem. Moreover, our approach (even without the IP effects) yielded an optimal solution within a wide class of computational algorithms that included the conventional time-domain finite-difference, discrete Fourier transform and spectral Lanczos decomposition methods. Numerical examples for the controlled-source EM problem showed that the new algorithm produces accurate solutions on time intervals spanning from milliseconds to hundreds of seconds with the cost of (at most) 60 time steps of the implicit finite-difference time domain scheme. This showed significant improvement even compared with results for nonpolarized media reported in recent literature. Additionally, the new algorithm had the unique capability to accurately handle large-scale 3D models, including the IP effects. [ABSTRACT FROM AUTHOR]

Published
2011
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28. Gauss-Arnoldi quadrature for and rational Padé-type approximation for Markov-type functions

Author

Knizhnerman, L A

Abstract

The efficiency of Gauss-Arnoldi quadrature for the calculation of the quantity is studied, where is a bounded operator in a Hilbert space and is a non-trivial vector in this space. A necessary and a sufficient conditions are found for the efficiency of the quadrature in the case of a normal operator. An example of a non-normal operator for which this quadrature is inefficient is presented.

Published
2008
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