Automatic generation of wave digital structures for numerically integrating linear symmetric hyperbolic PDEs (Q816081)

Numerical integration of partial differential equations by means of wave digital principles can be applied to passive physical problems. At first the author summarizes some known results on that approach. Especially, the used coordinate transformation and the passivity are explained. The properties of a system described by linear partial differential equations are examined. Necessary and sufficient conditions for passivity are given. Then, the conversion of a symmetric hyperbolic system into a discrete multidimensional passive system by using the generalized trapezoidal rule to all reactive elements and the wave quantities is described. Furthermore, a method to include the boundaries in the computations is presented. The described algorithm is well-suited for parallel computers.