Meep is a free finite-difference time-domain (FDTD) simulation software package to model electromagnetic systems. It supports distributed-memory parallel simulations, nonlinear, anisotropic, and dispersive media, PML absorbing boundaries, and 1D/2D/3D and cylindrical problems. It is completely scriptable from either C++ or a Scheme (GNU Guile) interface.
Meta.Numerics is a Mono-compatible .NET library for scientific and numerical programming. It includes functionality for matrix algebra (including SVD, non-symmetric eigensystems, and sparse matrices), special functions of real and complex numbers (including Bessel functions and the complex error function), statistics and data analysis (including PCA, logistic and nonlinear regression, statistical tests, and nonuniform random deviates), and signal processing (including arbitrary-length FFTs).
openEMS is an electromagnetic field solver using the FDTD method. It employs a fully 3D Cartesian and cylindrical coordinate graded mesh. Matlab (or Octave) is used as an easy and flexible scripting interface. Advanced Features include: multi-threading, SIMD (SSE), and MPI support for high speed FDTD.