The Essence of Scientific Computing

Scientific computing is the process of computing data to describe a scientific problem, which falls under the broad domain of computational science. This rapidly growing branch is an amalgamation of various branches of Science and Engineering and covers the various aspects of a complex problem.

Although computational science spans many different disciplines, at its core, the main methodology is developing a mathematical model that describes a natural system (with a variable amount of accuracy). The model is then solved using computation, and the result is interpreted to understand the phenomenon under consideration.

As the literature repeatedly points out, among the various advantages of scientific computing, one of the most important is that it allows for the study of phenomena inaccessible to orthodox experimental Science, either economically, practically, or both.

Various aspects of computational science can be broadly broken down into two main categories: –

1. Algorithm: Algorithms can be mathematical models describing the studied phenomenon. Most of the time, algorithms are based on concepts rooted in physics or can be mere computational tools resembling the real phenomenon. Still, nevertheless, they are mathematical descriptions of the phenomenon. The essence of scientific computing is the implementation of numerical algorithms (alternatively, computational mathematics).
2. Infrastructure: The computing infrastructure usually consists of the algorithm being converted into a program in any high-level programming language, depending on its efficiency. Various computational techniques, such as the segregation of the algorithm into various domains following the shared-memory or the distributed-memory framework, allow for parallelization of the program execution, resulting in less CPU time and, hence, faster execution of the code. The programs are usually executed in distributed computing platforms such as clusters consisting of multiple processors (usually hundreds of them) or even in supercomputers, which comes under the domain of High-Performance Computing (HPC).

The actual Science of combining the above-mentioned aspects of scientific computing to model a physical process and get the final results for analysis (post-processing) is usually termed Computer Simulation.

There are many fields in which Computational Science has made a strong impact, namely Computational Finance, Computational Biology, urban complex systems, Complex System Theory, and, relatively recently, computational Materials Science.

Phase-field modeling is one of the subdomains of Computational Science, which mainly deals with phenomena usually studied under Computational Physics, which leans more towards Materials Science. Although more phase-field models are being developed, they lack much real physics and serve as excellent mathematical/computational tools to study phenomena of phase transformations in more diverse materials like polymers, ceramics, etc.

Computational Science (or alternatively, scientific computing) is a sophisticated tool developed to advance Human Knowledge. Still, it comes with various limitations and constraints, which must be dealt with with the progress of technology. As processing power increases with time, the domain of Computational Science will render more problems tractable, which were deemed unsolvable by Physicists a couple of decades ago. The horizon of this field is increasing, giving rise to more and more exciting Science and a better understanding of the processes underlying the Natural world we see.

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