| Summary: | 碩士 === 國立成功大學 === 數學系應用數學碩博士班 === 102 === In this thesis, we suppose the molecular surfaces determined by free-energy of the implicit solvent model, and nd its steady state, in other words, to simulate the rational molecular surfaces. In the model, the speed of interface depends on the gradient of the electrostatic potential and its gradient which are derived from the elliptic interface problem. The interface is tracked and moved by the level set method and the elliptic interface problem is solved by coupling interface method on Cartesian grid. In this study, we propose oblique coordinate systems by changing variables at the exceptional points in order to approximate the second order derivatives accurately. As a result, we get second-order approximation for the solution and its gradient. The numerical tests for the coupling interface method with oblique coordinate systems show the secondorder approximation for the solution and its gradients. For moving interface problems, we show the second-order convergence for a moving spherical interface by the proposed method. At nal, we demonstrate the molecular surface of real molecule (1D63) by for complex interfaces by minimizing the free energy based on the implicit solvent model.
|
|---|
