臺灣博碩士論文加值系統

邊界元素法是用數值方法來解決二維線性化Poisson-Boltzmann方程. 這個方程模擬分子生物物理中離子在溶液勢能分佈. 我們在處理邊界元素法中的奇異積分時,引進去奇異的技巧, 而且用小波方法來對相關的線性系統作compression和preconditioning.

A boundary element method(BEM) is presented for solving the linearized Poisson-Boltzmann equation(LPBE) numerically. This equation is used to model the distribution of ions in molecular biophysics. We introduce a desingularization technique in dealing with the singular integral in the BEM formulation, and we use wavelet method for compression and preconditioning for solving the corresponding discrete linear system.

1. Introduction
2. Physical Model
2.1 The physical model
2.2 The nonlinear and linearized Poisson-Boltzmann equations
2.3 A symmetric solution of linearized Poisson-Boltzmann equation
3. Boundary Element Methods
3.1 Boundary element method for model problem
3.2 Boundary element method
3.3 Wavelet method
3.4 Numerical results
4. Conclusion

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