A Domain Decomposition Based Jacobi-Davidson Algorithm for Quantum Dot Simulation
In this paper, we develop an overlapping domain decomposition (DD) based Jacobi-Davidson (JD) algorithm for a polynomial eigenvalue problem arising from quantum dot simulation. Both DD and JD have several adjustable components. The goal of the work is to figure out if it is possible to choose the right components of DD and JD such that the resulting approach has a near linear speedup for a fine mesh calculation. Through experiments, we find that the key is to use two different coarse meshes. One is used to obtain a good initial guess that helps to achieve quadratic convergence of the nonlinear JD iterations. The other guarantees scalable convergence of the linear solver of the correction equation. We report numerical experiments carried out on a supercomputer with over 10,000 processors.
KeywordsFinite Volume Method Domain Decomposition Fine Mesh Coarse Mesh Correction Equation
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