Open Access

ARTICLE

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

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.

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Keywords

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