Finite Integration Technique
Finite Integration Technique for Electromagnetic Field Simulation · Also known as: FIT, Finite integration method
The Finite Integration Technique (FIT) is a numerical method for solving Maxwell equations on structured grids, formulating electromagnetics as a system of integral equations over grid cells. Introduced by Thomas Weiland in 1977, FIT bridges finite differences and finite elements, offering excellent accuracy, stability, and computational efficiency for a wide range of electromagnetic problems. FIT is the foundation of commercial solvers like CST Microwave Studio and is widely used in RF, microwave, and EMC engineering.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
FIT excels for broadband transient and frequency-domain analysis of RF/microwave devices: filters, antennas, waveguides, and cavities. Preferred when wide frequency ranges and fine geometric details matter. Stable unconditionally or with modest time-step restrictions. Less efficient for problems requiring very large computational domains (use asymptotic methods instead). Ideal for problems where accuracy and stability matter more than absolute speed.
Strengths & limitations
- Preserves electromagnetic energy and charge conservation exactly at discrete level
- Unconditionally stable or nearly stable depending on time-stepping scheme
- Handles arbitrary geometries, anisotropy, and complex boundary conditions naturally
- Excellent for transient and broadband frequency responses; no resonance issues
- Structured grids can be less efficient for complex curved geometries; often requires many grid cells
- Time-step limited by Courant condition (grid size must be fine relative to wavelength)
- Memory requirements large for 3D problems with high frequency or wide spatial extent
- Accuracy depends on adequate grid resolution; underresolution leads to poor results
Frequently asked
How does FIT compare to FDTD (Finite Difference Time Domain)?
Both use regular grids and time-stepping. FIT uses integral form (better energy conservation); FDTD uses differential form (simpler implementation). FIT is slightly more robust; FDTD is easier to code. Both have similar computational cost.
What is the Courant condition and why is it important?
The Courant condition limits time-step: Δt ≤ Δx/(c√3) (in 3D), where Δx is grid size and c is light speed. Violating it causes numerical divergence. Finer grids require shorter time-steps, increasing computation.
How do I choose grid resolution?
Rule of thumb: grid cells should be ≤λ/10 (λ = wavelength). For frequency sweeps, use λ_min (shortest wavelength). Start coarse, refine, and check convergence of results.
Can FIT handle lossy materials and frequency-dependent properties?
Yes. Conductivity is incorporated directly; lossy dielectrics are handled via causal material models. Frequency-dependent materials (e.g., plasma) can use Debye or Drude models within FIT.
Sources
- Weiland, T. (1977). A new method for the solution of Maxwell's equations. Zeitschrift für Naturforschung, 31(7), 861-873. link ↗
- Clemens, M., & Weiland, T. (2001). Discrete electromagnetism with the finite integration technique. Progress in Electromagnetics Research, 32, 65-87. DOI: 10.2528/pier00080103 ↗
- Weiland, T. (1996). Time domain electromagnetic field computation with finite difference methods. International Journal of Numerical Modelling, 9(4), 295-319. DOI: 10.1002/(sici)1099-1204(199607)9:4<295::aid-jnm240>3.0.co;2-8 ↗
How to cite this page
ScholarGate. (2026, June 3). Finite Integration Technique for Electromagnetic Field Simulation. ScholarGate. https://scholargate.app/en/electrical-engineering/finite-integration-technique
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Method of MomentsElectrical Engineering↔ compare
- S-Parameter AnalysisElectrical Engineering↔ compare
- Transmission-Line Matrix MethodElectrical Engineering↔ compare