Finite Element Modeling:
Modeling of linear, second-order boundary-value problems:
Fixed Point Iteration:
HMD contains an alternative method for solving boundary value problems. The technique is called a "cell grid". A rectangular mesh is created automatically by growing an assemblage of "cells" into a grid. Each cell may be thought of as containing its own little solver (actually a finite representation of a Green's function solution) whose boundaries are considered to be the values at its neighboring cells. The cell values are iterated until the desired accuracy is achieved. There is nothing new about the idea, but the implimentation was inspired by Stephan Wolfram's book, "A New Kind of Science". I started to think about using cellular automata for solving the classical potential theory problem, and then realized that the "rule" for such a cell would merely be the condition that the potential and its first derivative be continuous at the boundary. The HMD cell grid solver is not really a cellular automata program--but this is where the idea came from. The cell grid solver is currently the main focus of development. The finite element solver is reliable and familiar to the engineering community. But I find the finite element method is limited, for the most part, to a few common, linear problems. The cell grid solver will be able to solve nonlinear problems and, at some point, be amenable to a parallel processing architecture.
Approach:
HMD is oriented to the physicist and applied mathematician. Thus HMD is not limited to any one area of finite element analysis, such as structural engineering or fluid mechanics, etc. Physical problems are solved as general partial differential equations in which the the distinguishing physical features are embedded in the PDE coefficients (material coefficients) and the boundary conditions. With HMD you solve, for example, Poisson's Equation. This could be a structural strain problem, or an electrostatics problem, or a steady-state heat transfer problem depending on the coefficients and the coundary conditions. This makes HMD a versatile analysis tool, but it has the drawback of requiring you to know more about mathematical methods and about the finite element method.
Free Software Support:
The philosophy of HMD is to be just one component in a greater suite of free software tools. The use of the HMD program relies on the use of other free software tools to work: GMSH for generating the grid, Scilab for analysing and plotting the results, Gnuplot for plotting the results, GMV for displaying finite element surface plots, and Image Magick for displaying the image slices. HMD is a solver--a command line program that reads a script file. Support for other free software tools will be added in the future.