@Article{cmes.2005.008.001, AUTHOR = {C. K. Au}, TITLE = {A Geometrical Approach for Solving 2D Eikonal Equation}, JOURNAL = {Computer Modeling in Engineering \& Sciences}, VOLUME = {8}, YEAR = {2005}, NUMBER = {1}, PAGES = {1--14}, URL = {http://www.techscience.com/CMES/v8n1/29738}, ISSN = {1526-1506}, 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.}, DOI = {10.3970/cmes.2005.008.001} }