Finite Elements for Multiphysics

The Simulation Software openCFS

The modelling of mechatronic systems leads to so-called multifield problems, which are described by a system of nonlinear partial differential equations. The complexity consists of the simultaneous computation of the involved single fields as well as in the coupling terms, which introduce in most cases additional nonlinearities, e.g. moving/deforming conductive bodies within an electromagnetic field.

For the efficient solution of these multifield problems, we have developed within the last years the simulation software openCFS, opens an external URL in a new window (Coupled Field Simulation) based on the finite element (FE) method, which is continuously improved by new numerical schemes, advanced material models and coupling strategies. With a special focus on structural mechanics, acoustics, electromagnetics and heat transfer, CFS++ allows high-end computations of the following coupled fields:

  • electromagnetics-mechanics-acoustics
  • piezoelectrics-acoustics
  • electro-thermo-mechanics
  • electrostatic-mechanics-acoustics
  • aeroacoustics.
Field simulation for two elongated bodies as a simulation result
Model of a red micro antenna

Benefit of the Simulation Software openCFS

1. Higher Order Finite Elements

In addition to standard FE methods (isoparametric approximation) openCFS allows for high order elements, which guarantee optimal convergence rates and therefore computational efficiency

2. Flexible Discretisation

Nonconforming grid techniques can handle computational grids being considerably different in adjacent subdomains. Thereby, not only the numerical error can be strongly reduced, but also the pre-processing of complex  structures is significantly simplified.

3. Coupling Strategies

The software openCFS allows for both volume as well as surface coupling between different physical fields and performs a simultaneous solution of the coupled fields. Further openCFS is an integral part in almost all our industrial research projects and allows for efficient virtual prototyping.


Hassanpour Guilvaiee, Hamideh, Florian Toth, and Manfred Kaltenbacher. "A Non‐conforming Finite Element Formulation for Modeling Compressible Viscous Fluid and Flexible Solid Interaction, opens an external URL in a new window." International Journal for Numerical Methods in Engineering.

Schoder, Stefan, Florian Toth, Clemens Freidhager, and Manfred Kaltenbacher. "Revisiting infinite mapping layer for open domain problems, opens an external URL in a new window." Journal of Computational Physics 392 (2019): 354-367.

Roppert, Klaus, Florian Toth, and Manfred Kaltenbacher. "Simulating induction heating processes using harmonic balance FEM, opens an external URL in a new window." COMPEL-The international journal for computation and mathematics in electrical and electronic engineering 38, no. 5 (2019): 1562-1574.


Assistant Prof. Dipl.-Ing. Dr.techn. Florian Toth

Send email to Florian Toth