The harmonic balance (HB) method is one of the most commonly used methods for solving periodic solutions both weakly and strongly nonlinear dynamical systems. However, it confined to low-order approximations due complex symbolic operations. Many variants have been developed improve HB method, among which time domain HB-like are regarded as crucial improvements because their fast computation sim...

In this study, a hybrid method is proposed to investigate the nonlinear vibrations of pre- and post-buckled rectangular plates for the first time. This is an answer to an existing need to develope a fast and precise numerical model which can handle the nonlinear vibrations of buckled plates under different boundary conditions and plate shapes. The method uses the differential quadrature element...

high harmonic generation is a useful tool for the generation of short, intense attosecond pulses. In order to simulate high harmonic generation, we performed a numerical solution to the time dependent Schrödinger equation. by considering dipole approximation, we predicted generation of a 53 attosecond pulse. In order to see the time and frequency of emission of attosecond pulse, we exploit...

In this paper a new method is presented for the detection of chaotic responses using harmonic balance commercial simulators. The method is applicable to circuits exhibiting homoclinic bifurcation routes. The successive period-doublings, often preceding the formation of homoclinic orbits, are predicted and calculated. This is done by means of a new probe technique that overcomes the harmonic bal...

Rather than approach the parallelization of the harmonic balance simulation method numerically, a novel scheduling-oriented approach is described. The technique leverages circuit substructure to expose potential parallelism in the form of a directed, acyclic graph (dag) of computations. This dag is then allocated and scheduled using various linear clustering techniques. The result is a highly s...