Skip to content

Technology

μfem is built around a high–performance finite element core with a strong focus on scalability, automation, and reproducibility. The architecture is designed for large-scale simulation campaigns, research workflows, and industrial engineering applications.

Core Discretization Engine

μfem uses MFEM as its computational backbone.

  • High-order finite elements on unstructured meshes
  • Native support for H¹, H(curl), H(div), and L² spaces
  • Parallel domain decomposition with MPI
  • Algebraic multigrid and advanced preconditioners

This enables accurate large-scale simulations for electromagnetics and multi-physics problems.

High-Order Accuracy

μfem supports true high-order methods:

  • Curved (isoparametric) higher-order geometry
  • High-order basis functions
  • Consistent integration for nonlinear material models

This allows:

  • Reduced numerical dispersion
  • Improved convergence rates
  • Fewer elements for equivalent accuracy

High-order geometry is especially important for electromagnetic simulations with curved domains and rotating machinery.

Adaptive Mesh Refinement

μfem supports adaptive mesh refinement (AMR):

  • Local h-refinement
  • Hanging-node support
  • Parallel refinement workflows

This allows accurate resolution of:

  • Singular fields
  • Skin effects
  • Boundary layers
  • Localized nonlinearities

Native Python Interface

μfem provides a Python-first workflow:

  • Problem definition in Python
  • Direct access to model parameters
  • Seamless scripting and automation
  • Integration with NumPy and scientific Python ecosystem

This makes μfem suitable for:

  • Parameter sweeps
  • Optimization loops
  • Machine learning integration
  • AI-driven simulation pipelines

Performance Portability

μfem is designed for heterogeneous compute environments:

  • Multi-core CPUs
  • Distributed-memory clusters (MPI)
  • GPU-ready backend through MFEM

This enables scaling from:

  • Laptop prototyping
  • Workstation engineering studies
  • HPC cluster simulations

Cartesian Meshes & Implicit Geometry

μfem supports structured Cartesian meshes combined with implicit geometry descriptions.

  • Hex-dominant discretizations
  • Cut-cell integration workflows
  • Level-set driven material definitions
  • Efficient geometry parameterization

This is particularly powerful for:

  • Parametric studies
  • Topology variations
  • Optimization workflows
  • Geometry-driven automation