# Computational mechanics

Computational Mechanics is the discipline concerned with the use of computational methods to study phenomena governed by the principles of mechanics . Before the emergence of computational science (also called scientific computing) as a “third way” besides theoretical and experimental sciences, computational mechanics was widely considered to be a sub-discipline of applied mechanics . It is now considered to be a sub-discipline within computational science.

## Overview

Computational mechanics (CM) is interdisciplinary. Its three pillars are mechanics , mathematics , and computer science .

MECHANICS: Computational fluid dynamics , computational thermodynamics , computational electromagnetics , computational solid mechanics are some of the many specializations within CM.

MATHEMATICS: The areas of mathematics most closely related to computational mechanics and partial differential equations , linear algebra and numerical analysis . The most popular numerical methods are the finite element , the finite difference , and the boundary element methods in order of dominance. In favor of finite element methods, thermodynamics, and electromagnetism. The boundary element technique is in general, but has a niche in certain areas including acoustics engineering, for example.

COMPUTER SCIENCE: With regard to computing, computer programming, algorithms, and parallel computing play a major role in CM. The most widely used language in the scientific community, including computational mechanics, is Fortran . Recently, C ++ has increased in popularity. The scientific computing community has been slow in adopting C ++ as the lingua franca. MATLAB is also widely used, especially for rapid application development and model verification, because of its very natural way of expressing mathematical computations, and its built-in visualization capabilities.

## Process

Scientists within the field of computational mechanics

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 being adapted 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 or iterative methods (which starts with a trial solution and arrives 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 experimental results Either gold simplified models for qui exact analytical solutions are available. Quite frequently, new numerical or computational techniques are verified by comparing these 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 given to the results.

## Applications

Some examples where computational mechanics have been made to simulate vehicle simulation simulation , petroleum reservoir modeling , biomechanics, glass manufacturing, and semiconductor modeling.