陳宜良Chern, I-Liang臺灣大學:數學研究所李浩志Lee, Hao-ChihHao-ChihLee2010-05-052018-06-282010-05-052018-06-282008U0001-1607200813385800http://ntur.lib.ntu.edu.tw//handle/246246/180567腫瘤生長的邊界演進是個不穩定的過程。在數值模擬中，介面的演進對於自身的曲率通常相當敏感，因而導致了不正確的計算與不穩定性。在這篇論文中，我們提出一個奠基在最小平方法上的邊界速度延拓方法，這個方法搭配上等位函數法（Level set method），可以成功模擬連續的腫瘤生長模型，並達到二階精確度。The growth ofumor boundary is an unstable evolution process. In numericalimulation, the evolution of the boundary is technically veryensitive to its curvature, and causes numerical instability andncorrect calculation. In this paper, we propose a least-squareethod for the extension of the boundary velocity. This extension,ogether with the level set method, can compute a continuous modelor the tumor growth and achieve the second order accuracy.Acknowledgements pibstract (in Chinese) piibstract (in English) piiiontents pivigures pivables piv. Introduction p1.1. Derivation of Governing Equations p1.2. A Model of Nonnecrotic Tumor p4.3. Dimensionless Formulation p5.4. Introduction to Level Set Method p6. Numerical Methods p8.1. Main Loop p8.2. Notations p8. Solving Poisson Equation on Arbitrary Domain p9.1. Discretize Poisson equation over arbitrary domain p9.2. Finding intersection of interface and grid lines p11.3. Curvature Discretization and Interpolation p12. Level Set p14.1. Numerical Flux p14.2. Spatial Discretization p14.3. Temporal Discretization p16.4. Redistancing p16.5. Normal Vector p17. Treatment in Computing Velocity p18.1. Discretization of Prevelocity p18.2. Least Square Velocity Extension p19.3. Velocity Filtering p21. Numerical Results p23.1. Poisson Solver p23.2. Interface Propagator and Velocity Related 28.3. Overall Method p32. Conclusion p37. Appendix p38eferences p39application/pdf534653 bytesapplication/pdfen-US腫瘤生長等位函數法最小平方速度場延拓界面問題tumor growthlevel setleast squarevelocity extensioninterface evolutionthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/180567/1/ntu-97-R95221008-1.pdf