An improvement of level set equations via approximation of a distance function

Hamamuki Nao

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An improvement of level set equations via approximation of a distance function

机译：通过近距离函数的级别设置方程的改进

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In the classical level set method, the slope of solutions can be very small or large, and it can make it difficult to get the precise level set numerically. In this paper, we introduce an improved level set equation whose solutions are close to the signed distance function to evolving interfaces. The improved equation is derived via approximation of the evolution equation for the distance function. Applying the comparison principle, we give an upper- and lower bound near the zero level set for the viscosity solution to the initial value problem.

机译：在经典级别设置方法中，解决方案的斜率可以非常小或大，并且可以使得难以在数值上设置精确的水平。在本文中，我们介绍了一种改进的水平集等式，其解决方案靠近符号距离函数以不断变化的接口。通过距离函数的演化方程的近似来导出改进的等式。应用比较原理，我们在零水平设置附近的上限和下限为初始值问题。

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来源
《Applicable Analysis》 |2019年第12期|共15页
作者
Hamamuki Nao;
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作者单位

Hokkaido Univ Dept Math Sapporo Hokkaido Japan;

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原文格式 PDF
正文语种 eng
中图分类数学分析;
关键词
Level set method; improved level set equations; signed distance function; viscosity solutions;

机译：水平集方法;改进的水平设定方程;符号距离功能;粘度溶液;

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1. An improvement of level set equations via approximation of a distance function [J] . Hamamuki Nao Applicable Analysis . 2019,第9a12期

机译：通过近距离函数的级别设置方程的改进
2. How accurately can we calculate molecular CH and CC r_e distances by DFT methods? Dependence on basis sets and functionals, estimations of experimentally inaccessible r_e distances and distance-dependent scaling factors for approximations of triple-z [J] . Alexander Neugebauer, Gunter Hafelinger Journal of Molecular Structure. Theochem: Applications of Theoretical Chemistry to Organic, Inorganic and Biological Problems . 2002,第1a3期

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3. Constructible sets of linear differential equations and effective rational approximations of polylogarithmic functions [J] . Marc Huttner Israel Journal of Mathematics . 2006,第1期

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4. Review of Five Sets of Piecewise Constant Orthogonal Functions for Function Approximation, Integration and Solution of First Order Differential Equation Using These Function Sets [C] . A. Ganguly, H. Basu International Conference on Advances in Control and Optimization of Dynamical Systems . 2014

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5. Mathematical modeling of quantum dots with generalized envelope functions approximations and coupled partial differential equations. [D] . Sytnyk, Dmytro. 2010

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6. Solution of the chemical master equation by radial basis functions approximation with interface tracking [O] . Ivan Kryven, Susanna Röblitz, Christof Schütte 2015

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7. A level set method using the signed distance function (Numerical Solution of Partial Differential Equations and Related Topics) [O] . Kimura Masato 2000

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8. Trial Functions for the Space Dependence of the LIFE Fuel-Pin Performance Equations/Piecewise Cubic Polynomial Interpolation Approximations [R] . O'Reilly, B. D. 1975

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An improvement of level set equations via approximation of a distance function

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