What is Computational Science

The design, prototyping, optimization, and control of technological processes depend on fundamental understanding of the phenomena involved, their interactions, and sensitivity on parameters. These can be studied very effectively via computer simulations based on mathematical models expressing physical principles.

• Modeling: The first step is the "mathematization" of the process, namely the development of a mathematical model of the physical process. It is often by far the most difficult.
• Analysis: Then the full arsenal of mathematical tools can be used to analyze and understand the basic properties of the mathematical model and attempt to predict its behavior. This is where theoretical issues (existence, uniqueness, stability of solutions) become important, often generating challenging problems for theoretical mathematical research.
• Scientific Computing comes into play next, in developing appropriate and effective numerical methods for the mathematical problem.
• Programing: The algorithms are implemented in a high level computer language (Fortran, C, C++).
• Verification: The computer code is tested extensively on problems/processes with known solution/behavior. Bugs are corrected and the code is tested over and over.
• Optimization: The computer code is optimized for robustness, stability, and efficiency.
• Parallelization: Realistic problems are typically very demanding computationally, so parallelization of the code is necessary, to run on clusters of multiprocessors and/or many networked computers simultaneously.
• Validation: The final crucial step is validation of the model, by simulating a process and comparing the results of numerical simulations with experimental measurements. It may require several iterations of all the steps above !