Thomas Russell: Programmer & Designer
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Solution to the Poisson Equation in C++ using Successive Over-relaxation

Poisson Equation Plots

Note: The first section of this blog post is mathematical and useful to understand, however, if you are just looking for an implementation you can skip through to the first code block.

Due to the interest in my previous blog post: Solution to the Laplace Equation in C++ using successive over-relaxation, I have decided to write a follow-up post on how to extend the method to allow for solutions to the Poisson Equation.

The Poisson Equation is the general case of the Laplace Equation and takes the following form:

$$\nabla^{2} \phi = f(\vec{r})$$

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Solution to the Laplace Equation in C++ using successive over-relaxation

Note: The first section of this blog post is mathematical and useful to understand, however, if you are just looking for an implementation you can skip through to the first code block.

Partial Differential Equations are notoriously difficult to solve analytically; in all but the simplest cases, there often does not exist a solution in elementary form. This would be acceptable, but for the ubiquity of partial differential equations in physical models. So Mathematicians and Computer Scientists had to develop methods of solving PDEs numerically.

In this blog post, I will show one such method of solving Laplace’s equation (a type of PDE) in $\mathbb{R}^{2}$ using the method of successive over-relaxation, an iterative technique which involves splitting the relevant domain into a grid and sampling each point in a fixed order. For those who don’t know, or have forgotten, Laplace’s equation is written as follows:

$$\nabla^{2} \psi = 0$$

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Pebble App – App Manager

I recently got a Pebble as a present from my lovely girlfriend and I’ve been toying with the idea of creating an app for it, partly for fun and partly to support the awesome work that I think the guys at Pebble are doing.

I’m aiming to help resolve what I feel is one of the major issues with the Pebble framework at the moment, which is its fixed address app structure. For those who don’t know; you can currently only install a maximum of 8 apps/watchfaces on the watch at any one time regardless of how much space each app or watchface takes up, this means that whilst your Pebble has a storage capacity of 800KB, the majority of that space is likely wasted.

The primary goals of the app can be summarized as follows: Read more »

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