wave equation

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a differential equation that describes the passage of harmonic waves through a medium

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A model for sound wave propagation in a room with heterogeneous medium, for example, a screen in the room leads to more or less efficient method for solving the wave equation, for example using the Boundary Element Method (BEM) and finds an approximate solution to the wave equation by solving the system of equations resulting from discretizing the surfaces into patches.
Note that in this setting it is, of course, much simpler to calculate the wave function directly by solving the wave equation with numerically with finite elements.
Over the centuries, mathematicians have developed ways of solving the wave equation to determine the normal modes of various drum surfaces.