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J. Kruzik and D. Horak

¹IT4Innovations, VSB-Technical University of Ostrava, Czech Republic
²Department of Applied Mathematics, VSB-Technical University of Ostrava, Czech Republic

doi:10.4203/ccp.111.9

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J. Kruzik, D. Horak , "Wavelet Based Deflation of Conjugate Gradient Method", in P. Iványi, B.H.V. Topping, G. Várady, (Editors), "Proceedings of the Fifth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 9, 2017. doi:10.4203/ccp.111.9

Keywords: deflation, projected preconditioning, conjugate gradient, deflated conjugate gradient, wavelet compression, coarse problem, Krylov subspace.

Summary

This paper introduces a Krylov subspace deflation technique based on a discretewavelet compression. This technique is based on an observation that the deflation coarse problem matrix is closely related to a matrix obtained by a discrete wavelet transformation. Thanks to this observation, we know exactly how the deflation space should look like. Moreover, we can directly and cheaply assemble this space. We showcase both numerical and performance aspects of our approach on the deflated conjugate gradient method. However, our findings should be also valid for other deflated Krylov subspace methods, like GMRES or MINRES.

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 111 PROCEEDINGS OF THE FIFTH INTERNATIONAL CONFERENCE ON PARALLEL, DISTRIBUTED, GRID AND CLOUD COMPUTING FOR ENGINEERING Edited by: P. Iványi, B.H.V. Topping and G. Várady Paper 9 Wavelet Based Deflation of Conjugate Gradient Method J. Kruzik and D. Horak ¹IT4Innovations, VSB-Technical University of Ostrava, Czech Republic ²Department of Applied Mathematics, VSB-Technical University of Ostrava, Czech Republic doi:10.4203/ccp.111.9 purchase the full-text of this paper Full Bibliographic Reference for this paper J. Kruzik, D. Horak , "Wavelet Based Deflation of Conjugate Gradient Method", in P. Iványi, B.H.V. Topping, G. Várady, (Editors), "Proceedings of the Fifth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering", Civil-Comp Press, Stirlingshire, UK, Paper 9, 2017. doi:10.4203/ccp.111.9 Keywords: deflation, projected preconditioning, conjugate gradient, deflated conjugate gradient, wavelet compression, coarse problem, Krylov subspace. Summary This paper introduces a Krylov subspace deflation technique based on a discretewavelet compression. This technique is based on an observation that the deflation coarse problem matrix is closely related to a matrix obtained by a discrete wavelet transformation. Thanks to this observation, we know exactly how the deflation space should look like. Moreover, we can directly and cheaply assemble this space. We showcase both numerical and performance aspects of our approach on the deflated conjugate gradient method. However, our findings should be also valid for other deflated Krylov subspace methods, like GMRES or MINRES. purchase the full-text of this paper (price £22) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £45 +P&P)
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