Computational Mechanics - Process

Process

Scientists within the field of computational mechanics follow a list of tasks to analyze their target mechanical process:

1. A mathematical model of the physical phenomenon is made. This usually involves expressing the natural or engineering system in terms of partial differential equations. This step uses physics to formalize a complex system.

2. The mathematical equations are converted into forms which are suitable for digital computation. This step is called discretization because it involves creating an approximate discrete model from the original continuous model. In particular, it typically translates a partial differential equation (or a system thereof) into a system of algebraic equations. The processes involved in this step are studied in the field of numerical analysis.

3. Computer programs are made to solve the discretized equations using direct methods (which are single step methods resulting in the solution) or iterative methods (which start with a trial solution and arrive at the actual solution by successive refinement). Depending on the nature of the problem, supercomputers or parallel computers may be used at this stage.

4. The mathematical model, numerical procedures, and the computer codes are verified using either experimental results or simplified models for which exact analytical solutions are available. Quite frequently, new numerical or computational techniques are verified by comparing their result with those of existing well-established numerical methods. In many cases, benchmark problems are also available. The numerical results also have to be visualized and often physical interpretations will be given to the results.