Introduction to scientific computing and computational geodynamics

Present life without computers is almost impossible: industry and agriculture, government and media, transportation and insurance are major users of computational power. The earliest and still principal users of computers are researchers who solve problems in science and engineering or more specifically, who obtain solutions of mathematical models that represent some physical situation. The methods, tools and theories required to obtain such solutions are together called scientific computing, and the use of these methods, tools and theories to resolve scientific problems is referred to as computational science. A majority of these methods, tools, and theories were developed in mathematics well before the advent of computers. This set of mathematical theories and methods is an essential part of numerical mathematics and constitutes a major part of scientific computing. The development of computers signalled a new era in the approach to the solution of scientific problems. Many of the numerical methods initially developed for the purpose of hand calculation had to be revised; new techniques for solving scientific problems using electronic computers were intensively developed. Programming languages, operating systems, management of large quantities of data, correctness of numerical codes and many other considerations relevant to the efficient and accurate solution of the problems using a large computer system became subjects of the new discipline of computer science, on which scientific computing now depends heavily.