Because Finite Element and Boundary Element methods used to simulate cone loudspeaker directivity are slow and demanding on memory, this research explores the use of mode matching methods. A mode matching method for simulating concave, axisymmetric geometries offers a viable alternative. This method is based on a method presented by Pagneux et al. for simulation of horns, but has been extended so that vibrating walls can be taken into account. With the previous method it was possible to find impedance, pressure, and volume velocity by working step by step from one end of the structure to the other. With the new method, pressure and volume velocity at all points in the structure are found simultaneously by solving a large but sparse linear system of equations. Two examples of loudspeaker diaphragm shapes demonstrate how the method could be used to optimize diaphragm shape.
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