The importance of inverse laws has been acknowledged in various branches of
science and technology for a long time. Whenever, a
particular physical phenomenon is modeled using sources or sinks, the inverse
laws come into play. These laws are found to be crucially
important in
gravitation, electromagnetics, ideal fluid dynamics, Stoke's flow, acoustics,
optics,
thermodynamics and many other fields. In fact, a large part of the classical
physics, when assumed non-dissipative, can be described by some form of the
inverse laws such as the Laplace's and Poisson's equations. These two linear
second order partial differential equations have been considered to be among
the most important differential equations in the whole of classical physics.
While the effect of point sources and sinks can be easily computed, it has not
been possible to obtain closed form expressions for computing the effects of
distributed sources, except for very simple cases. But, since in many
of the real-life problems the singularities are found to
be distributed on surfaces of various shapes and sizes, it has been customary to
represent them using the simple shapes for which closed form expressions are
known, or simply by assuming the surface to be composed of a large number of
point sources. These approximations, besides being computationally rather
expensive, turn out to be significantly restricted and inaccurate.
The ISLES (inverse square law exact solutions) library allows us to compute the
influence of distributed singularities on rectangular and triangular flat
elements. As a result, the neBEM (nearly exact Boundary Element Method) solver
based on this library, can solve the Poisson's equation in 3D efficienty to a
very high degree of accuracy. Due to the availablity of both rectangular and
triangular elements, the solver is flexible enough to solve problems involving
complicated geometries.