A Geometrical Approach for Solving 2D Eikonal Equation

C. Au

doi:10.3970/cmes.2005.008.001

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A Geometrical Approach for Solving 2D Eikonal Equation

C. K. Au¹
1 School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore

Computer Modeling in Engineering & Sciences 2005, 8(1), 1-14. https://doi.org/10.3970/cmes.2005.008.001

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Abstract

Solving the Eikonal equation is popular due to its potential applications in various areas. Numerical method is the most common approach to solve the equation. This paper presents a geometric approach to solve the equation. Each point in a two dimensional domain with a given velocity field is characterized by the least time from the source. The path of least time is obtained by the Euler equations characterizing the extrema of the variation problem. A geometric representation of the space time function for the source is constructed. The solution to the eikonal equation is obtained based on space time geometry.

Keywords

path of least time, eikonal equation, front propagation

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Au, C. K. (2005). A Geometrical Approach for Solving 2D Eikonal Equation. CMES-Computer Modeling in Engineering & Sciences, 8(1), 1–14.

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