New Adaptive Mesh Refinement (AMR) in CADFEKO
Altair EmployeeNew Adaptive Mesh Refinement (AMR) in CADFEKO
Automatic mesh adaptation to find trade-off between model size and accuracy
Feko simulations are using a meshed representation to describe geometry of a model. The simulation method is needing the mesh elements to define local basis functions for describing physical quantities like e.g. surface currents in the Methods of Moments (MoM). Feko supports different kind of mesh elements: Segments, triangles, tetrahedra and voxels.
One of Feko’s strengths are the multiple solvers that can be hybridized with each other. Since different solvers have different pros and cons, the hybridization cleverly exploits the advantages of individual approaches.
This can be demonstrated for the horn antenna with waveguide: The air-filled waveguide and the anisotropic circulator are modeled better with volume elements of Finite Element Method (FEM) using tetrahedron elements.
The horn itself is modelled with classical Method of Moments (MoM) using triangle elements on the surface of the antenna. And finally, the dielectric glass lens and the absorber is modeled using the Surface Equivalence Principle (SEP) of MoM. For higher frequencies (or larger object size) the Multi-Level Fast Multipole Method (MLFMM) could be used instead of MoM.
The fineness of the mesh has an influence on the simulation accuracy and the calculation effort. A compromise must therefore be found to have sufficient accuracy with a mesh model as lean as possible. For classical MoM and MLFMM simulation with 2D surface meshes Feko has for many years built in automatisms that create the necessary element size when the simulation frequency is specified. Also, local mesh refinements near sources and along edges are set fully automatically.
For volume meshes with the finite element method (FEM) the situation is a bit more challenging. Local mesh refinement of tetrahedra elements in a 3D volume is more complex than local mesh refinement of triangle elements on a 2D surface. For tetrahedral elements, the mesh refinement rules are much more model-dependent and therefore it makes sense to determine iteratively an optimal local mesh refinement using error estimation.
Since Feko2023 the new tool AMRFEKO is available, which enables automatic adaptive mesh refinement based on error estimates for FEM and MoM/FEM solutions. The fully automatic tool can be launched from a command prompt or any of the Feko GUIs and can also be used on HPC resources in a similar fashion to RUNFEKO. In the CADFEKO GUI the new AMRFEKO feature is integrated into the Solve/Run tab:
Patch antenna example
We demo the adaptive mesh refinement feature for a patch antenna modeled with FEM. The antenna is evaluated in the frequency range from 2.8 GHz to 3.1 GHz. To minimize the number of boundary elements between the FEM region and the free space MoM region a FEM air box is used.
Mesh settings have big influence on number of tetrahedron elements in the FEM region. There is a surprisingly high factor of 72 between the element numbers for a fine and coarse model. In such a case a trade-of between model size and simulation accuracy is beneficial and can be realized with AMRFEKO. With the coarse mesh memory requirements and runtimes are very good, but the model is not able to capture the resonance frequency accurately.
With the fine mesh results are correct with the price of higher memory requirements and much longer runtime. In the third variant AMRFEKO creates a mesh with local refinements that is sufficient to compute accurate results. Runtime has improved by factor 24 and memory by factor 6 compared to the variant with fine mesh.
You can download the Feko model files (version 2024.1) to do your own tests.
Additionally I recommend a tutorial video on this topic in the Altair How-To Youtube Channel.