Multidimensional wave-digital principles: from filtering to numerical integration

Wave-digital principles, originally developed for one-dimensional filtering purposes, have later been extended to multidimensional filtering applications and have been shown to be applicable also to numerical integration of physically relevant ordinary and partial (thus multidimensional) differential equations of linear and nonlinear type. They are based on physical concepts such as Kirchhoff circuits, wave quantities, energy and power, passivity etc. They offer a number of advantages such as good stability and, more generally, high robustness (ensured by the availability of a suitable Liapunov function), and proper interpretability in the spectral domain. To these can be added in the multidimensional case, especially for numerical integration of partial differential equations, massive parallelism, full locality, and ease to take into account space- and time-varying parameters and arbitrary boundary shapes and conditions. In the present paper, a brief survey of the method is offered for the multidimensional case