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The Westervelt equation is a model for the propagation of finite amplitude ultrasound. The method of discrete exterior calculus can be used to solve this equation numerically. A significant advantage of this method is that it can be used to find numerical solutions in the discrete space manifold and the time, and therefore is a generation of finite difference time domain method. This algorithm has been implemented in C++.
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Xie et al. (2010) studied this question.