Scientific computing is the scientific discipline that deals with the modelling and computer-based numerical simulation of complex processes that appear within natural, engineering, economical and social sciences. Scientific computing supplements the two classical pillars of knowledge acquisition within the respective applied sciences, namely the theoretical investigation and the laboratory experiment. This discipline with its methodologies of modelling, numerical simulation and optimisation has developed to a key technology for the understanding and handling of scientifical and technological challenges. Such different and complex problems like the design of the shape of a wing, the modelling and visualization of electrical excitation waves in the brain and heart muscle tissues, the design and control of nano and micro systems, etc., require scientific computing methodologies. With scientific computing it is possible to discover new features of real systems as with challenging experiments in a physics or chemistry laboratory.