This is the M.I.T. link for FastCap, FastHenry and FastImp *nix source files distribution.
This is the direct link to the M.I.T. CAD group, where FastCap and FastHenry were developed. Throught this link you can reach the pages containing the original docs and the papers presenting the algorithms implemented in the software.
Whiteley Research offers a completely free graphical editor and design tool for integrated circuit mask layout, schematic capture, and much more, and a companion Spice circuit simulation tool, for *nix and Windows. All the software is also available in Open Source. Parasitic extraction is available through FasterCap, FastCap and FastHenry.
LTSpice is a free, analog / digital Spice-based simulator for Windows with schematic entry and waveform post-processor from Linear Technology. Very useful free tool to run circuit simulations on the results of your field solvers extractions.
Ngspice is an open-source (BSD license), free, multi-platform (Windows, Linux, MacOS), analog / digital Spice-based simulator.
It is an evolution of the original Berkeley SPICE3F5, integrated with XSPICE
(for mixed-signal simulation), and including TLCSpice (a TCL/TK interface).
Ngspice is also integrated in the free gEDA suite of Electronic Design Automation tools available for Linux and MacOS.
Qucs is a promising open-source (GLP license), free, multi-platform (Windows, Linux, MacOS) circuit simulator. Qucs provides a GUI for schematic entry and for showing simulation results in various types of diagrams. It supports DC, AC, S-parameter, noise and transient analysis is possible. It allows mathematical equations and use of a subcircuit hierarchy (with parameterised subcircuits) are available. Qucs can also import existing SPICE models.
Scilab is free and open source software for numerical computation providing a powerful computing environment for engineering and scientific applications. It is a very valid replacement for Matlab.
Maxima is an open source, free system for the manipulation of symbolic and numerical expressions. It is the right companion for SciLab.