1926 to 1937, Feng Kang studied in the experimental primary school, junior high school and senior high school affiliated to Suzhou Middle School in Jiangsu Province. 1939 was admitted to the Department of Electrical Engineering of Central University (1949 was renamed Nanjing University), and two years later he was transferred to the Department of Physics, majoring in electrical engineering, physics and mathematics. 1944 graduated from Chongqing Central University. 1946 teaching in Tsinghua University.
195 1 worked in Institute of Computing Technology, Chinese Academy of Sciences, during which 195 1 to 1953 studied in Czechoslovakia Institute of Mathematics, Soviet Union, 1957 to 1978 served as an associate researcher in Institute of Computing Technology, Chinese Academy of Sciences. 1978- 1987 was the director of the Computing Center of China Academy of Sciences, and 1987 was the honorary chairman of the Center. The finite element method, naturalisation method and natural boundary element method are independently created, which opens up a new field of symplectic geometry and symplectic scheme research.
In the research of basic mathematics, he has made contributions to topological group structure and generalized function theory. In applied mathematics and computational mathematics, it has guided and solved many difficult problems in national economy and national defense construction. Independent of the west, a modern system calculation method for solving elliptic differential equations-variational difference method, that is, finite element method, is established. This achievement won the second prize of 1982 National Natural Science Award. Feng Kang also put forward the natural integral equation of elliptic equation and the natural coupling method of finite element boundary element, and developed the symplectic geometric numerical solution of Hamiltonian dynamic system.
Feng Kang contributed.
As early as the 1960s, when introducing his research methods, Feng Kang once said: "My research on computational mathematics started not from reading other people's papers, but from the principles of engineering or physics."
After Feng Kang successfully established the finite element method, he put forward the symplectic geometry algorithm of Hamiltonian system, which opened up a brand-new research field and had broad application prospects. Why does he want to do research in this direction? In the invitation report of 199 1 annual meeting of the Chinese Physical Society, Feng Kang raised some scientific questions about the dynamic system: What will the solar system look like in the distant future? In what orbit will the planet run? Will the earth collide with other planets?
Some people may think that as long as Newton's law is used, a program is compiled according to the existing calculation method, and then a supercomputer is used for calculation. After a long time, the result can always be obtained. But can such a calculation result be believed? In fact, for such a complicated calculation, the computer can either get no result at all or get a completely wrong result. Even if the error of each step is small, the accumulated error will make the result unrecognizable! This is a problem of calculation method, no matter how good the machine performance is, no matter how high the programming technology is.
The dynamic system problem is different from the elliptic boundary value problem, and the finite element method can not solve this kind of problem well. What kind of calculation method should be used to calculate the problem of dynamic system? In the process of establishing the finite element method, Feng Kang realized that various equivalent mathematical expressions of the same physical process may lead to inequality in calculation methods. The success of finite element method for elliptic boundary value problems is due to the selection of appropriate mechanical system and mathematical form.
The finite element method can't solve the dynamic problem well, because the Lagrangian mechanical system can't reflect its essential characteristics well. So Feng Kang returned to the principles of physics. The classical mechanical equation, which ranks first in mathematical physics equations, has three equivalent mathematical formal systems: Newton mechanical system, Lagrangian mechanical system and Hamiltonian mechanical system. Among them, Hamiltonian system has always been the starting point of physical theory research, and its application involves many fields such as physics, mechanics and engineering. However, until the early 1980s, the calculation method of Hamilton system was still blank.
Why can't we develop a new calculation method from Hamiltonian system? So Feng Kang began to study in this direction. He found that only Hamiltonian mechanical system is the most suitable mechanical system for studying dynamic problems. Because symplectic geometry is the mathematical basis of Hamiltonian system, Feng Kang grasped the breakthrough of designing numerical method of Hamiltonian system-symplectic geometry method with his unique mathematical intuition. He organized a research team to conduct systematic theoretical research and extensive numerical experiments on symplectic geometry algorithm of Hamiltonian system. After more than ten years of unremitting efforts, he finally achieved extremely fruitful results.
At present, the known traditional algorithms are almost not symplectic algorithms, so it inevitably brings the defects of distorted system characteristics such as artificial dissipation. However, many symplectic algorithms proposed by Feng Kang and others have maintained the architecture, and have unique advantages in stability and long-term tracking ability, and have been successfully applied in the calculation of dynamic astronomy, atmospheric ocean, molecular dynamics and other fields in China.
In-depth theoretical analysis and a large number of numerical experiments convincingly show that symplectic algorithm solves the long-term prediction and calculation problems of dynamics. The appearance of this new algorithm has even changed the research methods of some disciplines and will be widely used in more fields.
Feng Kang's personal honor
Practice is the only criterion for testing truth. Thankfully, with the passage of time, Feng Kang's scientific achievements are more and more recognized by people, and his great contributions are highlighted in many fields.
1in the spring of 997, Professor China Academy of Sciences, a winner of Fields Prize, made a report entitled "My Opinions on the Development of Mathematics in China" in Tsinghua University, and mentioned that "there are three main reasons why China's modern mathematics can surpass or keep pace with the West, mainly because there are three famous ones in the history of mathematics: one is the professor's work in demonstration classes, and the other is China's work in multiple changes.
This highly evaluation of Feng Kang as a mathematician (not just a computational mathematician) is refreshing. To this end, many people have a strong resonance with each other, although their statements are likely to surprise some people.
Subsequently, at the end of 1997, the first prize of National Natural Science was awarded to another work by Feng Kang, Symplectic Geometry Algorithm of Hamilton System, which was a belated consolation prize and a further affirmation of his scientific achievements.
Feng Kang's profound cultural accomplishment.
Scientists, of course, are not stars falling from the sky, but mortals on the earth, who have gradually grown up through the cultivation and exercise of family, school and society.
Feng Kang's profound cultural accomplishment is attributed to middle school education. His alma mater, the famous Suzhou Middle School, obviously played a great role. From the family point of view, it is mainly to provide a relaxed learning environment and atmosphere. "Relaxation" is very important, which is in sharp contrast with today's situation.
When Feng Kang first entered junior high school, he met with difficulties in English. Because he didn't learn English at all in primary school, most of his classmates have learned English. The solution of the problem depends entirely on our own efforts, and soon caught up with the whole class. Not only that, but also jumped to the forefront of the class. Throughout this period, he studied easily and happily, instead of studying hard as emphasized by China's traditional education, and never burned the midnight oil (which was completely different from his later situation), even during the examination. At that time, middle school education emphasized "English, Chinese and mathematics" as the foundation. Here is a brief introduction.
Suzhou Middle School is a provincial middle school. English is limited to classroom teaching, and there is no oral training. He learns English well in class and pays attention to self-study after class. During the third year of senior high school, he often translated some literary works from Selected English of Senior High School into Chinese. I remember that a humorous article "Training in the Boudoir" was published in Yijing magazine, and another drama "Starting from the Month" was not published. When War of Resistance against Japanese Aggression started, the school library was bombed. He once found an English book "Collection of the World's Great Novelists" among the ruins and ashes. He read some chapters with relish, which was the beginning of his reading of English books and periodicals. English newspapers and movies have also become his auxiliary means of learning English. Later, he gave lectures in fluent English at many international conferences and communicated with foreign scholars. He has never received formal oral English training, relying on the basis of classroom teaching in middle schools and later reading and using more.
As for other foreign languages, he studied Russian specially and lived in the Soviet Union for several years. German is the second foreign language learned in college, and you can read books and periodicals smoothly; French is self-taught, and a set of records was used to learn French conversation in the late Cultural Revolution.
Generally speaking, his foreign language literacy is outstanding. He can not only read scientific literature in a narrow sense, but also read books related to science in a wide range of fields, such as memoirs, biographies, historical materials, and scientists' comments. These experiences enabled him to read the world extensively and broaden his horizons, so his views on science were superb.
On the other hand, the nourishment of culture also brought comfort and fun to his bumpy life. 1944, when he was bedridden and his future was bleak, he got comfort from reading Shakespeare's Hamlet, recited poems and monologues for a long time and tirelessly appreciated them.
He studied Shakespeare and Gibbon in English, Tolstoy in Russian, Zweig in German and Baudelaire in French. The original soup is unique. As a result, he cleansed his mind, cultivated his sentiment, broadened his horizons, and made him stand upright in the most difficult years.
Speaking of Chinese, he also has a good foundation. Both classical Chinese and vernacular Chinese are taught in middle schools, but classical Chinese is the main one. He can write in simple classical Chinese. I remember that at the end of the Cultural Revolution, when there were no books to read, he bought a set of four histories (Historical Records, Hanshu, Houhanshu and the History of the Three Kingdoms) to entertain himself. Obviously, his Chinese literacy has also played a very good role in his future work. Feng Kang's scientific reports, even lectures, are deeply loved by the audience because of its vivid, concise and logical language. His articles and lectures also reflect this feature.
As for mathematics, not only did he get excellent grades in class, but he also studied and solved problems with reference to Fan's Algebra and other original foreign textbooks. It should be said that his middle school mathematics foundation is very solid. It is also worth mentioning that there is a popular science book that has a far-reaching influence on him.
In senior three, he carefully read Zhu Yanjun's "From Mathematics". Zhu is a senior mathematician in China. He studied at the University of G? ttingen and taught at Shanghai Jiaotong University after returning to China. This book introduces what modern mathematics is through the dialogue between scholars and businessmen (including Fermat's Last Theorem, Goldbach and other issues). This book has a strong appeal, which opened Feng Kang's eyes, caught a glimpse of the magical world of modern mathematics for the first time, and was deeply fascinated by it. This may be an opportunity for Feng Kang to devote himself to mathematics and aspire to become a mathematician. Of course, the road is not smooth.
Feng Kang's broad professional foundation.
Feng Kang's college career was full of twists and turns, which attracted people's attention. As Professor Lax said, "Feng Kang's early education was electrical engineering, physics and mathematics, and this background imperceptibly formed his later interest." Pointed out a rather critical problem. As an applied mathematician, the foundation of engineering physics is very important.
Feng Kang's experience can be said to be the most ideal way to train applied mathematicians. Although it was not a conscious choice and arrangement, it was an accidental encounter. /kloc-in the autumn of 0/938, I moved to Fujian with my family, taught myself at home for half a year, and read Sabendong's General Physics. 1939 In the spring, I went to the Department of Mathematics and Physics of concord college in Shaowu, northwest Fujian. /kloc-in the summer of 0/939, he was admitted to the Department of Electrical Engineering of Central University. This may be related to the trend of the times at that time.
Electrical engineering is considered to be the most useful and the best way out. At that time, students flocked to become the most competitive and difficult department. He also has a young competitive spirit. The more difficult it is, the more he wants to try. In addition, the influence of big brother Feng Huan (he is a graduate of electrical engineering department of Central University) may also be a factor. In this way, he was admitted to the Department of Electrical Engineering of CUHK with the first place. After entering the school, I gradually felt that engineering seemed tasteless and could not satisfy his intellectual thirst. So I want to change from engineering to science, and the goal is physics department.
Because it was put forward too late, it has not been converted to the second grade, which leads to the situation of studying two departments at the same time, and studying the main courses of the Department of Electricity and the Department of Physics. It causes a heavy burden and has a negative impact on the body. At this time, spinal tuberculosis has begun to show signs. On the plus side, his engineering training is relatively complete.
In the third and fourth grades, he almost finished all the main courses of physics department and mathematics department. In this process, his interest shifted from physics to mathematics. It is worth noting that in the 1940s, as the climax of mathematical abstraction (represented by Bubaki School), this trend also spread to students interested in mathematical science in China University. They have an unrealistic sense of knowledge snobbery. Science is higher than engineering, mathematics occupies the highest position in science, and the more abstract mathematics itself, the better. Feng Kangzhi turned from industry to science, from physics to mathematics, and he tended to pure mathematics in mathematics, which is the embodiment of this trend of thought.
He took a detour in the subject, which is really beneficial to his future development in applied mathematics. Imagine that if you go directly to the department of mathematics, although you have to take some physics classes, because of the psychological obstacles above, it will have little effect, let alone engineering. At present, the voice of broadening university majors is rampant, and the case of Feng Kang can give some enlightenment to this.
Shortly after graduating from college, Feng Kang suffered from spinal tuberculosis. He was ill at home because he had no money to stay in hospital. From1May 1944 to1September 1945, it was the most difficult period in his life. In his hospital bed, he still studied the classic works of modern mathematics tirelessly.
Feng Kang indulged in it day and night and enjoyed it tirelessly, which made him forget his personal illness and the sinister environment around him. This enterprising spirit in mathematics not only further consolidated the foundation, but also connected with the new frontier of contemporary development, which made his understanding of modern mathematics reach a higher level. /kloc-in the summer of 0/946, his wound miraculously healed and he was able to stand up. Later, he went to Fudan University to teach, and he continued to teach himself.
Feng Kang's Two Major Scientific Breakthroughs
It is usually impossible to make a major breakthrough in science. Vision, ability and opportunity are indispensable. Feng Kang achieved two major scientific breakthroughs in his life, which are very valuable and worth writing about. First, from 1964 to 1965, the finite element method was established independently, which laid its mathematical foundation; The second is the symplectic geometry algorithm of Hamiltonian system created after 1984 and its development. At present, scientific innovation has become the focus of discussion. We might as well take Feng Kang's two breakthroughs as cases of scientific innovation. It is particularly worth emphasizing that these two breakthroughs were discovered by China scientists on the land of China. A serious case analysis of it remains to be done by experts.
These two breakthroughs are not only due to Feng Kang's mathematical attainments, but also closely related to his mastery of classical physics and engineering technology. Scientific breakthroughs often have interdisciplinary characteristics. Another point to emphasize is that there are several years of gestation before the breakthrough. It is not advisable to be quick and quick because of the need to accumulate wealth.
The opportunity of finite element method comes from a national key task, that is, the calculation problems involved in Liujiaxia dam design. Faced with such a specific practical problem, Feng Kang found a basic problem with keen eyes.
He thinks that the method of dealing with mathematical discrete calculation should be divided into four steps: (1) defining physical mechanism, (2) writing mathematical expression, (3) adopting discrete model and (4) designing algorithm. However, traditional methods may be ineffective for problems with complex geometric and physical conditions. Therefore, he considered whether he could go beyond the convention and not write down the differential equations describing physical phenomena, but directly relate to the appropriate discrete model from the conservation law or variational principle in physics.
In the past, Euler, Rayleigh, Ritz, Paulia and other masters all considered this method, but these were before the advent of electronic computers. Combined with the characteristics of computer calculation, the variational principle is directly linked with the difference scheme to form the finite element method, which has wide adaptability and is especially suitable for dealing with engineering calculation problems with complex geometric and physical conditions. The implementation of this method began with 1964, which solved specific practical problems. 1965, Feng Kang published the article "Difference Scheme Based on Variational Principle", which is the main basis for the international academic circles to recognize the independent development of finite element method in China. However, it is a great pity that the evaluation of Feng Kang's great contribution is late and insufficient.
In the 1970s, the finite element method was transplanted from abroad. At the meeting, some people openly sarcastically said, "There is such a strange saying that the finite element method was invented by China people." At the meeting, Feng Kang had to shut up. This fact was told to me by Feng Kang himself. Later, there were more international contacts. Visiting French mathematician Lyons and American mathematician Lax both acknowledged Feng Kang's achievements in developing finite element method independently of foreign countries, and the ice was finally broken.
After the Cultural Revolution, although he continued to work in the related fields of finite element, and had many outstanding achievements, such as discontinuous finite element method and boundary normalization method, he began to look for the next breakthrough. He paid attention to and understood the new trends in the boundary between mathematics and physics, and read a lot of literature.
Arnold's Mathematical Problems of Classical Mechanics came out in the 1970s, and expounded the symplectic geometric structure of Hamilton equation, which greatly inspired him and made him find a breakthrough. His long-term practice in computational mathematics has enabled him to deeply understand different mathematical expressions of the same physical law, although they are physically equivalent; But they are not equivalent in calculation (his students call it von's theorem), so Newton equation, Lagrange equation and Hamilton equation in classical mechanics show different modes in calculation. Because Hamilton equation has symplectic geometry structure, he is keenly aware that if the symmetry of symplectic geometry can be maintained in the algorithm, the defects of artificial dissipation algorithm can be avoided and it will become a high-fidelity algorithm. In this way, he opened up a broad way to deal with the calculation of Hamiltonian system, which he nicknamed Hamilton Avenue, and was widely used in the orbital calculation of celestial mechanics, orbital calculation in particle accelerators and molecular dynamics calculation.