![]() ![]() Once again for a 1 dimensional system, this reduces to the two equations: Where B k is the k th spatial component of the magnetic field. The third equation can be written out more clearly as: In order to implement the FDTD algorithm, we only need to use the third and fourth equations. Where Ḃ and Ė are the time derivatives of the magnetic field and electric field respectively. In this post, we will explore how to implement the one dimensional electromagnetic FDTD algorithm in Python.Īs this post focuses on electromagnetism, we start from Maxwell’s equations in Gaussian units, and scale the units such that the value of the speed of light c = 1, and assume that no current J is present in the system: Such equations are impossible to solve analytically for complex systems such as random lasers or volcanic systems, and scientists have to make use of numerical methods to better understand how such systems behave under various conditions. The finite difference time domain (FDTD) algorithm is a numerical method used to solve partial differential equations which have both spatial and temporal derivatives such as Maxwell’s equations or seismic waves propagating through the earth. Please check here for the latest version of this post. Update: due to various difficulties encountered in writing Python code and mathematical equations in WordPress, I have decided to start migrating most of my content to Github. ![]()
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