Robust discretization algorithms for the numerical intergration of nonlinear PDEs with application to a generalized capacitor

Abstract

Numerical integration of nonlinear (NL) partial differential equations (PDEs) is studied via approximating the original continuous-domain physical system by a discrete multidimensional (MD) and passive system, using principles of wave digital filters. Resulting integration algorithms are highly robust, massively parallel, imply only local interconnections. The numerically integrated system of NL PDEs is a special case of the Maxwell's equations, namely the system of two conductor plates separated by dielectric. Inductance, capacitance and resistance coefficients are appropriate nonlinear functions of the currents, voltage, space and time.