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Harmonic balance method for multiphysics simulation

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

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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

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Fourier representation

Fields are expressed as a truncated Fourier series (constant + sine/cosine terms at selected harmonics).
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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.
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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.
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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.

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Case example

Nonlinear systems in the frequency domain with harmonic balance

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

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Case example

Optimizing designs by simulating thousands of design variations

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

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“Quanscient Allsolve provides effortless scaling of compute power, enabling examination of larger design spaces for the most critical parameters. It allows us to advance with MEMS speaker designs we truly trust and to scale our development effectively.”

Nilavazhagan Subbiah, PhD — Staff Engineer, Infineon

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