Introduction

Purpose of the neBEM toolkit is to help users solve scientific / technological problems governed by the three-dimensional Laplace's / Poisson's equation. At the end of a successful solution, the user is left with a distribution of singularities that satisfies the boundary conditions of the problem as specified by the user. The procedure that needs to be followed can be described as a three-step one: i) Pre-processing, ii) Solution, iii) Post-processing. The three steps are being described below in brief.

Pre-processing: The geometry of the problem and various material properties (such as the conductor / dielectric nature, potential etc for an electromagnetic problems), amount of discretization or the level of accuracy required etc are specified. These information can be specified using a separate software (e.g., Garfield) or a small independent code or can be directly built into the mandatory interface code. The geometry of the problem is described by wires (1D) and flat surfaces (2D), the latter being rectangular or right triangles at present, arbitrary polygons to be implemented very soon! The wires and flat surfaces used to describe a given physical system are called primitives.

Solution: The real hard work is done here. Possible steps are discretization of the primitives into smaller wire, triangular or rectangular elements on which it is reasonable to assume uniform singularity distribution, setting up of the influence coefficient matrix, its inversion, setting up the right-hand side (RHS) vector and finding the solution. The influence coefficient matrix depends on the geometry, various material properties and remains unchanged for a given device despite a change in the boundary conditions. That is why, we invert the influence coefficient matrix as soon as it is made and keep it stored for use with various possible boundary conditions. The RHS depends on the boundary conditions specified and can be modified while keeping the geometry and other properties of the problem unchanged. The solution (e.g., the charge density in an electrostatic problem) is obtained by multiplying the inverted influence coefficient matrix to the RHS.

Post-processing: The solution is used to estimate necessary properties at any location or to carry out some other estimation, such as finding out the capacitance or force on a component for an electrostatic device. It is quite normal to invoke only the post-processing part of the computation repeatedly for a given device, on which the singularity density distribution has been estimated earlier. This is the reason neBEM has the provision to store each solution for a given device model and boundary conditions.