The Benefits of FFT-based Preconditioner in Numerical Simulations of 3D Photonic Crystals
Date Issued
2012
Date
2012
Author(s)
Chang, Hao-Chieh
Abstract
This thesis aims to implement the solver of the eigenvalue system Ax = λBx on computer with multi-core CPUs. The problem derived from the Maxwell equations which is 3D diamond photonic crystals. The matrix A is a irregularly large-scale sparse matrix, so how to solve the eigenvalue system more efficient is a challenge. Because using the shift and invert eigenvalue solver, we need to solve the linear system. We provide a very powerful preconditioning scheme to accelerate the linear system. A suitable preconditioner makes the linear system converge quickly and more stable. The code are implemented by using some packages such as Intel Math Kernel Library (MKL), PETCs and SLEPc. Finally, we will show our numerical results and analysis the effect on multi-core CPUs.
Subjects
Maxwell equations
Three-dimension photonic crystals
Diamond structure
Preconditioner
Fast fourier transform
Eigenvalue problems
Type
thesis
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