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標題: 多重網格-共軛梯度法處理反應-擴散系統
Multigrid-conjugate gradient type methods for reaction-diffusion systems
作者: 陳慧霜
Chen, Jessica
關鍵字: 反應-擴散系統;reaction-diffusion systems;延續法;分歧點;有限差分法;多重網格法;continuation methods;bifurcation;finite differenes;multigrid methods;Bi-CGSTAB;GMRES
出版社: 應用數學系

We study multigrid methods in the context of continuation methods for reaction-diffusion systems, where the Bi-CGSTAB and the GMRES methods are used as the relaxation scheme for the V-cycle, W-cycle and full approximation schemes, respectively. In particular, we apply the results of Brown and Walker [1997] to investigate how the GMRES method can be used to solve nearly singular systems that occur in continuation problems. We show that for the sake of switching branches safely, one would rather to solve a perturbed problem near bifurcation points. We propose several multigrid-continuation algorithms for curve-tracking in nonlinear elliptic eigenvalue problems. Our numerical results show that the algorithms we propose have the advantage of being robust and can be easily implemented.
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