What is Advanced Computing?

Scientific computing refers to the entire process of using computers to reproduce, predict, and discover the laws and evolution characteristics of the objective world. Scientific computing Numerical calculations using computers to solve mathematical problems in science and engineering.

Scientific calculation is numerical calculation. Scientific calculation refers to the mathematical calculations encountered in the application of computer to scientific research and engineering technology. In modern science and engineering technology, a large number of complex mathematical calculation problems are often encountered. These problems are very difficult to solve with general calculation tools, but it is very easy to handle them with computers.

The laws of natural science are usually expressed by various types of mathematical equations. The purpose of scientific calculation is to find the numerical solutions of these equations. This kind of calculation involves a huge amount of calculations, and simple calculation tools are incompetent. Before the advent of computers, scientific research and engineering design relied mainly on data provided by experiments or experiments, and calculations were only in an auxiliary position. The rapid development of computers has made it possible for more and more complex calculations. The use of computers for scientific calculations has brought huge economic benefits, and has also caused a fundamental change in science and technology itself: traditional science and technology include only theoretical and experimental components. After using computers, computing has become an equally important third. Components.

It mainly includes the three stages of establishing mathematical model, calculating method of calculation and computer realization.

Establishing a mathematical model is to establish a series of quantitative relationships, that is, a set of mathematical formulas or equations, based on the relevant subject theory. Reasonable simplification of complex models is an important measure to avoid excessive calculations. Mathematical models generally include

Since the early 1970s, various scientific computing software products have gradually appeared. They are basically divided into two categories: one is for mathematical problems

What is scientific computing? Roughly speaking, scientific computing refers to the use of

Traditional theoretical research is based on analytical methods, which play an important role in the establishment of scientific principles and systems, and can solve relatively simple problems, such as linear problems and balance problems. However, as the problems become more complex With the increase of nature, the limitations of theoretical research are becoming more and more obvious. Many problems, such as strong nonlinear problems, non-equilibrium problems, and problems that occur in practical applications, have traditionally been powerless in traditional theoretical research. Compared with theoretical research, science Computation can not only handle linear and equilibrium problems, but more importantly, it can handle strong non-linear problems, non-equilibrium problems, etc., and can apply scientific principles to solve more and more complex practical problems. Scientific computing is also often called Computer virtual experiment. Compared with experimental research, scientific computing has at least the following three characteristics: one is no damage. In other words, scientific computing will not have a large impact on the environment, etc. This advantage makes scientific computing able to undertake real experiments. Things that cannot be done, such as studying the damage of a tsunami, the damage of an earthquake, the damage of a nuclear explosion Practical experiments, but scientific calculations and computer virtual experiments can be performed. The second is the whole process, all time and space diagnosis. Real experiments, no matter how many methods and how many instruments are used, the information about system evolution is very limited and difficult to do. To the whole process, all time and space diagnosis. And the whole process, all time and space information is extremely critical for people to understand, understand and control the research object. Unlike real experiments, scientific calculation can complete the whole process, all time and space diagnosis. As long as the application program Relevant output programs are added in.When performing scientific calculations, researchers can obtain all the information about the development and evolution of the research object at any time and any place, so that researchers can fully understand and carefully understand the development and research of the research object. Evolution. Third, scientific calculations can be carried out repeatedly and carefully in a short period of time in a relatively low-cost manner to obtain comprehensive and systematic information about the research object under various conditions. ^[1]

Vigorously develop basic algorithms for large-scale scientific computing

Scientific computing capabilities include the ability of computer hardware equipment and application software and algorithms that support the software. A 2005 report by the President's Advisory Committee on Information Technology states: "Although significant increases in processor performance are widely known, improved algorithms and libraries have contributed so much to improving computational simulation capabilities, just as improvements in hardware." As an example, three-dimensional Laplace equations are widely used in scientific computing applications. From the Gaussian elimination method in the 1950s to the multigrid method in the 1980s, the improvement of the algorithm makes the calculation amount proportional to the number 7 of the grid number N. The power of / 3 is reduced to the optimal calculation amount proportional to N. For N equal to 1 million, the calculation efficiency is improved by 100 million times! The WTEC report published by the United States World Technology Evaluation Center in 2009 evaluated applications that received the prestigious Gorden Bell award for supercomputing from 1998 to 2006, noting that although the application areas of the award-winning programs are different, the common point is that algorithms (linear Advances in algebra, graph splitting, region splitting, and higher-order discreteness have made the Gorden Bell award-winning application contribute more to computing power than Moore's Law. ^[2]

The numerical simulation problems to be solved by current scientific calculations are often very complicated, which brings great challenges to the study of numerical methods. The prominent common difficulties currently facing numerical method research are: high dimensionality, large calculation scale, multiple spatiotemporal scales, strong non-linearity, ill-posedness, long time, singularity, complex geometry, high morbidity, and high accuracy requirements. High-performance computers can solve these difficulties. The difficulty of numerical simulation is often manifested in an unbearably large scale or loss of timeliness; the algorithm does not converge or error accumulates the results beyond recognition; when a large number of computers are spent, no results are obtained or only incorrect results are obtained; the calculation is abnormal due to the singularity of the problem Aborting; the problem is too complicated to make the algorithm difficult to implement, etc. These difficult issues have received widespread attention in recent years, and have become a research hotspot in scientific computing. ^[2]

Vigorously develop high-performance scientific computing application software platforms and frameworks

The current high-performance computer architecture is becoming increasingly complex. CPU / GPU heterogeneity, thousands of computing nodes, multiple processors within nodes, multiple cores within processors, multi-core components within cores, and multi-level storage are its significant features. The development of the challenge. At present, the development of scientific computing application software in China is facing two major bottlenecks: first, the computing efficiency is low, and applications usually only play less than 10% of the peak performance of hundreds of processor cores; second, the long development cycle and high-performance computers Rapid development mismatch. Without breaking through these two bottlenecks, the development of parallel application software in China will be difficult to keep up with the development speed of high-performance computers. The advancement of computer technology cannot be effectively used for scientific and technological innovation, and it will not be able to exert its application in major national application fields. Valuable. ^[2]

In order to break through the two bottlenecks of "low computing efficiency" and "long development cycle", in recent years, Chinese scientists have proposed a new parallel software development method of "integration in common and supporting individuality" based on the multilayer software architecture of parallel applications. Based on this new idea, JASMIN, a three-dimensional parallel structure adaptive software framework, and PHG, a three-dimensional parallel adaptive finite element software platform, have been developed. These two platforms are based on basic common algorithms (such as grid adaptive and hundreds of processor cores). Solver) shields users from the details of parallel implementation, and solves the load balancing problem in adaptive parallel implementation. It has realized efficient parallel computing on several 10 trillion domestic parallel computers. ^[2]

With the support of the framework and platform, scientific computing researchers in various professional fields can focus on innovative research on physical models and computing methods. Without understanding the details of parallel computing, they can quickly integrate new physical models and computing methods into large-scale In parallel computing, researchers of computer systems can focus on the development of higher-speed and larger-scale computer systems without having to take into account the details of implementing specific scientific and engineering calculations. ^[2]

Vigorously strengthen the development of independent high-performance computing scientific software

The important feature of high-performance scientific computing application software is multi-disciplinary interdisciplinary, which is a combination of basic disciplines such as mathematics, physics, mechanics and corresponding application disciplines and computer software technology. It is based on algorithms and is a knowledge-intensive computer system. The integrated information products are highly specialized in the field. Only by establishing a high-level multi-disciplinary research team, after a long period of accumulation and precipitation for actual scientific problems, can they be successfully developed.

High-level computational science software requires advanced algorithms. We recommend that special attention be paid to the independent development of high-performance computational science software in the implementation of major national scientific and technological projects, and encourage more computational mathematics workers to dive into bottlenecks in scientific computing such as material computing. , Fluid computing, electromagnetic field computing, radiative fluid mechanics computing, algorithm research in nanocomputing and biocomputing, analysis and calculation of multi-scale models, and non-equilibrium computing, etc., the innovation of the algorithm should be combined with a model suitable for computing. ^[2]