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Harmonic balance method

Nonlinear frequency analysis via harmonic balance & cloud computing

Current flow   •   Heat solid   •   Solid mechanics   •   Electrostatics   •   Laminar flow   •   Mesh deformation   •   Fluid-Structure Interaction

The challenge

Nonlinear systems (like AC Joule Heating, Geometric Nonlinearity in Beams, or Electrostatic Speakers) are notoriously slow to simulate using traditional Time-Domain methods.

Engineers must wait for thousands of time steps for the system to reach a "steady state," and extracting frequency data (like Harmonic Distortion) from noisy transient results is difficult and error-prone.

Approach with Quanscient Allsolve

Quanscient Allsolve implements the Harmonic Balance Method (HBM) on the cloud—a technique that solves directly in the frequency domain, skipping the long transient wait time.

The platform enables HBM for fully coupled multiphysics (Fluid-Structure-Electrostatics), allowing engineers to capture higher-order harmonics and nonlinear distortions instantly.

Key results

  • Speed & clarity: Demonstrated on a Microspeaker, HBM captured Total Harmonic Distortion (THD) directly without transient noise.
  • Parallel efficiency: Ran a 75-point Frequency/Voltage sweep (20Hz–20kHz) in just 12 minutes using cloud parallelization.
  • Complex physics: Successfully modeled geometric nonlinearity (Beam Backbone Curves) and Joule Heating (2f harmonic components) that are difficult for standard frequency solvers.
The total harmonic distortion as a function of driving frequency and voltage.