Skip to content
Close
Talk to an expert
Japanese
Talk to an expert
Japanese

Harmonic balance method for multiphysics simulation

Fast, accurate steady‑state analysis of nonlinear multiphysics systems—directly in the frequency domain.

Talk to an expert
hb mockup with background v2

Why harmonic balance?

Go straight to steady state in the frequency domain—no long, noisy transients.

Capture higher harmonics created by nonlinearities for a complete picture of system behavior.

Focus on dominant harmonics to cut computation time.

Ideal for complex FEM multiphysics where traditional transient runs are slow or unstable.
The harmonic balance method

How it works

5 (1)
Fourier representation

Fields are expressed as a truncated Fourier series (constant + sine/cosine terms at selected harmonics).
See case examples
MUTs website content (6) (1)
Nonlinear balance

The method solves for harmonic coefficients that satisfy the governing equations and couplings at steady state—even when new harmonics are generated by nonlinearity.
7 (1)
Targeted accuracy

Choose only the harmonics that matter; reconstruct time‑signals from harmonic data when needed.
Quanscient Allsolve

Cloud-powered multiphysics simulation platform

Cloud‑scale FEM

On‑demand memory and cores remove hardware bottlenecks for large models and many harmonics.
True multiphysics

Run harmonic balance across coupled physics (e.g., electrostatics, solid mechanics, fluid, heat) with mesh deformation and geometric nonlinearity.
Selective harmonics

Analyze higher harmonics without simulating all intermediate ones to save compute.
Productivity at scale

Parallel parameter sweeps (frequency, voltage, load) for rapid design space exploration and metrics like THD.

FAQ

When should I use harmonic balance instead of transients? When you need steady‑state periodic behavior (including higher harmonics) without simulating long transients, or when nonlinear responses make time‑domain convergence difficult.
Can it handle nonlinearity and deformation? Yes—geometric nonlinearity, mesh deformation (ALE), and multiphysics couplings are supported.
How many harmonics should I include? Start with the fundamental and expected nonlinear products; add orders only if they materially impact accuracy.
Can I still view time‑domain fields?

Yes. Reconstruct time‑dependent signals over a period from the solved harmonic coefficients.
How does it scale? Cloud resources scale memory and cores for large DoF counts and broad parameter sweeps. Performance depends on model size, physics, and chosen harmonics.
harmonic-balance-2-1

See how Allsolve could work for you

Get in touch with us now to see how Allsolve can help with your specific challenges
Get in touch now
Resources

Case examples and other resources

White paper

Accelerating MEMS simulations with the harmonic balance method

See examples of the harmonic balance method applied to real-world use cases.

Open white paper →

Case example

Nonlinear systems in the frequency domain with harmonic balance

A comprehensive overview of the method with further details and other examples.

Open the article →

Case example

Optimizing designs by simulating thousands of design variations

Explore a case study covering running thousands of simulations in parallel with Quanscient Allsolve.

Open the article →

Abstract-mesh-3
Quanscient Allsolve

See how it could work for you

Submit the form to talk with our experts—we'll respond within 1 business day. You'll learn:

  • How Allsolve could fit your use case
  • What results to expect (accuracy, runtime, design exploration capabilities and rough cost range)
  • How it could plug into your workflow today

Interested in just seeing an on-demand demo? Watch the 3-minute demo here