ICTS Seminar
Title : A hybrid Krylov subspace method for FFT-based homogenisation of periodic media Speaker : Nachiketa Mishra, IISc, Bangalore
Date : Tuesday, December 29th, 2015 Time : 3 : 00 PM
Venue : Emmy Noether Seminar Room, ICTS Campus, Bangalore
Abstract : The FFT based homogenization from high resolution images, proposed by Moulinec and Suquet in 1994, is faster and requires less memory compared to finite element methods. The method is based on an iterative solution for the Lippmann Schwinger type integral equation for the unit cell problem of periodic homogenization. Recently [1], the method has been interpreted as a Galerkin scheme generating a system of linear equations for an unknownx∈E⊂EL
JL
U=Rn in the formCx=b with b=GAu and G=F−1GFˆ whereG∈Rn×n is an orthogonal projection from Rn toE expressed in terms of the inverse and forward Fourier transform matrices F−1, F ∈Rn×n, a block-diagonal matrix ˆG∈Rn×n, block-diagonal A∈Rn×n stores the problem coefficient, and u∈Uis a given vector. In this talk, I will discuss the different convergence properties of the hybrid Krylov solver when applied to the linear system.
Acknowledgments: This work was supported by the European Union under project #. CZ.1.07/2.3.00/30.0034.
References
[1] J. Vondˇrejc, J. Zeman, and I. Marek. An FFT-based Galerkin method for homogenization of periodic media.
Computers & Mathematics with Applications, 63(3):156–173, 2014.
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