Abstract
The equations of three-dimensional linear acoustics are formulated using a complex state vector and a first-order Lagrangian. Local conservation equations for energy, linear momentum, and angular momentum are derived in a unified and systematic way from gauge transformations. The first-order Lagrangian description is shown to lead naturally to a set of discrete space and discrete time field equations. Gauge transformations are again used to derive local conservation equations for the discrete field variables. Dispersion relations for the discrete equations are derived, and are used to analyze the spatial isotropy of propagating waves on the discrete space-time lattice. The solution of the discrete initial value problem is discussed, as well as its implementation on a massively parallel computer.
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