Opera-3d Static Electromagnetics Module

Opera-3d is a finite element (FE) software suite for electromagnetic (EM), thermal and structural simulations. Opera’s range of solver modules, including the 2d Static Electromagnetics Module (Static Module) can calculate magneto- and electrostatic fields and DC current flow in EM devices and systems. (This solver was formerly called TOSCA).

Static Module solver

Used extensively in scientific and engineering applications, the Static Module computes magnetostatic and electrostatic fields or DC current flow in three dimensions. It uses the FE method to solve Maxwell’s equations for the static case in a discretized model. For magnetostatics, the algorithms used in the Static Module automatically treat volumes in the model which contain magnetic sources differently to volumes without sources. By using this powerful method, the module successfully avoids cancellation errors that may occur using alternative solution methods. As a result, the accuracy of the solution is often far higher than would be expected from an FE analysis and this is proved by many years of comparison with measured results.

In this module users can specify magnetic material properties as linear, non-linear, isotropic, anisotropic, laminated or permanent magnet. Users are able to simulate coils/solenoids with extreme accuracy using Opera’s proprietary method which deploys the Biot-Savart integral to calculate magnetic fields from coils. Opera-3d includes a helpful library for easy definition of standard shapes, such as solenoids and racetracks, and also offers users the flexibility to create coils of any topology. Using the “lossy dielectric” option, users can simulate electric fields resulting from charging of low-conductivity dielectrics.

The program uses a sophisticated iterative solution technique to calculate the potential at each node of the mesh. This method offers great memory efficiency and high computer speed for users. Memory requirements are typically 5GB per 10 million finite elements. For example Opera-3d has been used to run a static EM calculation with 120 million elements on a computer with 60GB memory.

Opera is a multi-physics software suite which allows users to perform coupled simulations. This includes the ability to couple a Static Module simulation with a thermal simulation or a stress simulation, for example to calculate the stress due to electromagnetic forces.

Modeller and Post Processor

Opera-3d includes a geometric modeller that is used for model data definition, and a geometric post-processor for results analysis. The Graphical User Interface (GUI) gives access to features that have been specifically tailored for electromagnetics and multi-physics design. Regularly performed actions can be programmed into parameterized macro-files.

The Modeller allows users to create models, define material properties, set boundary conditions and excitations, create the mesh and launch the calculation. It allows the user to build models from primitive shapes using Boolean operations, or to import geometry from other CAD programs for which a range of I/O filters is available. Material data can be selected from a library of characteristics or input from the user’s own data.

The Opera-3d mesh generator has facilities for creating hexahedral, prism and tetrahedral meshes (the mesh can be a mixtures of types). Meshing is automatic, requiring little or no user setting in many cases. However, it does include facilities to finely control the mesh when required.

Solutions are stored in a database that can be interrogated using the Post Processor.


Opera-3d will run on Windows and Linux platforms A parallel option is available for shared memory computers.
H-Frame Dipole


  • Motors
  • Generators
  • Recording Heads
  • Electron Lenses
  • MRI Systems
  • Corrosion Protection
  • Scientific Apparatus
  • Electromagnetic Shielding
  • Fusion Magnets
  • Particle Accelerators
  • Magnetic signatures
  • Electrode systems


  • Full 3d modelling
  • Electrostatic field analysis
  • Charging of dielectrics (optional)
  • Magnetostatic field analysis
  • DC current flow
  • Linear and non-linear materials
  • Laminated materials
  • Isotropic and anisotropic materials
  • Permanent magnets
  • Conductors independent of mesh
  • Interfaces to CAD/CAM
  • Extendible Post-Processing

Results processing

  • 3D model views from any angle
  • Graphs, histograms and contour maps of the solution
  • Contours of the results on any surface
  • Calculation of fields, forces and energy
  • Charged particle tracking
  • User defined functions
  • Surface and volume integrals
  • Harmonic analyses