Feng Kang
Encyclopedia
Feng Kang (September 9, 1920 - August 17, 1993) was a Chinese mathematician
and scientist
.
He was born in Nanjing
, China
and spent his childhood in Suzhou
, Jiangsu
. He studied at Suzhou Middle School. In 1939 he was admitted to Department of Electrical Engineering
of the National Central University
(which moved to Chongqing
during 1937~1945 and changed the name to Nanjing University
in 1949 and reinstated in Taiwan
in 1962) and two years later he transferred to the Department of Physics
where he studied until his graduation in 1944. He got interested in mathematics
and studied it at the university.
After graduation he contracted vertebral tuberculosis and continued to learn mathematics
by himself at home. Later in 1946 he went to teach mathematics at Tsinghua University
. In 1951 he was appointed as assistant professor at Institute of Mathematics of the Chinese Academy of Sciences. From 1951 to 1953 he worked at Steklov Mathematical Institute in Moscow
, under the supervision of Professor Lev Pontryagin. In 1957 he was elected as an associate professor at Institute of Computer Technology of the Chinese Academy of Sciences
, where he began his work on computational mathematics and became the founder and leader of computational mathematics and scientific computing in China. In 1978 he was appointed as the first Director of the newly founded Computing Center of the Chinese Academy of Sciences until 1987 when he became the Honorary Director.
, specially on topological groups, Lie group
s and generalized function theory. From 1957 he changed to applied mathematics
and computational mathematics
. Because of his sound and broad knowledge in mathematics and physics, he made a series of pioneer researches in computational mathematics.
In the later 1950s and early 1960s, based on the computations of dam constructions, Professor Feng proposed a systematic numerical method for solving partial differential equations. The method was called Finite difference method based on variation principle (基于变分原理的差分方法). This method was also independently invented in the West, called there the finite element method
. It is now considered that the invention of the finite element method is a milestone of computational mathematics. In the 1970s Professor Feng gave embedding theories in the discontinuous finite element space, and generalized classical theory on elliptic equations to various dimensional combinations, which provided a mathematical foundation for elastic composite structures.
Also in the 1970s, he made great efforts and contributions in reducing elliptic equation to boundary integral equation. He gave natural boundary element method, which is now regarded as one of three main boundary element methods. From 1978 he had given lectures and seminars on finite elements and natural boundary elements in more than ten universities and institutes in France
, Italy
, Japan
and USA.
From 1984 Professor Feng changed his research field from elliptic equations to dynamical system
s such as Hamiltonian system
s and wave equation
s. He proposed symplectic algorithms for Hamiltonian systems based on symplectic geometry. Such algorithms can preserve the symplectic geometric structure of Hamiltonian systems.
He then led and supervised a research group on the symplectic algorithms for Hamiltonian systems with finite and infinite dimensions, and on dynamical systems with Lie algebra
ic structures, such as contact systems, source-free systems, etc., making use of the corresponding geometry and the underlying Lie algebras and Lie groups. These algorithms are overwhelmingly superior to conventional algorithms in long term tracking and qualitative simulation in many practical applications, such as celestial mechanics
, molecular dynamics
, etc.
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and scientist
Scientist
A scientist in a broad sense is one engaging in a systematic activity to acquire knowledge. In a more restricted sense, a scientist is an individual who uses the scientific method. The person may be an expert in one or more areas of science. This article focuses on the more restricted use of the word...
.
He was born in Nanjing
Nanjing
' is the capital of Jiangsu province in China and has a prominent place in Chinese history and culture, having been the capital of China on several occasions...
, China
China
Chinese civilization may refer to:* China for more general discussion of the country.* Chinese culture* Greater China, the transnational community of ethnic Chinese.* History of China* Sinosphere, the area historically affected by Chinese culture...
and spent his childhood in Suzhou
Suzhou
Suzhou , previously transliterated as Su-chou, Suchow, and Soochow, is a major city located in the southeast of Jiangsu Province in Eastern China, located adjacent to Shanghai Municipality. The city is situated on the lower reaches of the Yangtze River and on the shores of Taihu Lake and is a part...
, Jiangsu
Jiangsu
' is a province of the People's Republic of China, located along the east coast of the country. The name comes from jiang, short for the city of Jiangning , and su, for the city of Suzhou. The abbreviation for this province is "苏" , the second character of its name...
. He studied at Suzhou Middle School. In 1939 he was admitted to Department of Electrical Engineering
Electrical engineering
Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...
of the National Central University
National Central University
National Central University is a national comprehensive university in Taiwan .National Central University was founded in 1915 and originated in 258 CE at Nanjing, China. After NCU in Nanjing was renamed Nanjing University in 1949, NCU was re-established in Taiwan in 1962...
(which moved to Chongqing
Chongqing
Chongqing is a major city in Southwest China and one of the five national central cities of China. Administratively, it is one of the PRC's four direct-controlled municipalities , and the only such municipality in inland China.The municipality was created on 14 March 1997, succeeding the...
during 1937~1945 and changed the name to Nanjing University
Nanjing University
Nanjing University , or Nanking University, is one of the oldest and most prestigious institutions of higher learning in China...
in 1949 and reinstated in Taiwan
Taiwan
Taiwan , also known, especially in the past, as Formosa , is the largest island of the same-named island group of East Asia in the western Pacific Ocean and located off the southeastern coast of mainland China. The island forms over 99% of the current territory of the Republic of China following...
in 1962) and two years later he transferred to the Department of Physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
where he studied until his graduation in 1944. He got interested in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and studied it at the university.
After graduation he contracted vertebral tuberculosis and continued to learn mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
by himself at home. Later in 1946 he went to teach mathematics at Tsinghua University
Tsinghua University
Tsinghua University , colloquially known in Chinese as Qinghua, is a university in Beijing, China. The school is one of the nine universities of the C9 League. It was established in 1911 under the name "Tsinghua Xuetang" or "Tsinghua College" and was renamed the "Tsinghua School" one year later...
. In 1951 he was appointed as assistant professor at Institute of Mathematics of the Chinese Academy of Sciences. From 1951 to 1953 he worked at Steklov Mathematical Institute in Moscow
Moscow
Moscow is the capital, the most populous city, and the most populous federal subject of Russia. The city is a major political, economic, cultural, scientific, religious, financial, educational, and transportation centre of Russia and the continent...
, under the supervision of Professor Lev Pontryagin. In 1957 he was elected as an associate professor at Institute of Computer Technology of the Chinese Academy of Sciences
Chinese Academy of Sciences
The Chinese Academy of Sciences , formerly known as Academia Sinica, is the national academy for the natural sciences of the People's Republic of China. It is an institution of the State Council of China. It is headquartered in Beijing, with institutes all over the People's Republic of China...
, where he began his work on computational mathematics and became the founder and leader of computational mathematics and scientific computing in China. In 1978 he was appointed as the first Director of the newly founded Computing Center of the Chinese Academy of Sciences until 1987 when he became the Honorary Director.
Academic life
Feng Kang's scientific contributions range many fields. Before 1957 he mainly worked on pure mathematicsPure mathematics
Broadly speaking, pure mathematics is mathematics which studies entirely abstract concepts. From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics, and at variance with the trend towards meeting the needs of...
, specially on topological groups, Lie group
Lie group
In mathematics, a Lie group is a group which is also a differentiable manifold, with the property that the group operations are compatible with the smooth structure...
s and generalized function theory. From 1957 he changed to applied mathematics
Applied mathematics
Applied mathematics is a branch of mathematics that concerns itself with mathematical methods that are typically used in science, engineering, business, and industry. Thus, "applied mathematics" is a mathematical science with specialized knowledge...
and computational mathematics
Computational mathematics
Computational mathematics involves mathematical research in areas of science where computing plays a central and essential role, emphasizing algorithms, numerical methods, and symbolic methods. Computation in the research is prominent. Computational mathematics emerged as a distinct part of applied...
. Because of his sound and broad knowledge in mathematics and physics, he made a series of pioneer researches in computational mathematics.
In the later 1950s and early 1960s, based on the computations of dam constructions, Professor Feng proposed a systematic numerical method for solving partial differential equations. The method was called Finite difference method based on variation principle (基于变分原理的差分方法). This method was also independently invented in the West, called there the finite element method
Finite element method
The finite element method is a numerical technique for finding approximate solutions of partial differential equations as well as integral equations...
. It is now considered that the invention of the finite element method is a milestone of computational mathematics. In the 1970s Professor Feng gave embedding theories in the discontinuous finite element space, and generalized classical theory on elliptic equations to various dimensional combinations, which provided a mathematical foundation for elastic composite structures.
Also in the 1970s, he made great efforts and contributions in reducing elliptic equation to boundary integral equation. He gave natural boundary element method, which is now regarded as one of three main boundary element methods. From 1978 he had given lectures and seminars on finite elements and natural boundary elements in more than ten universities and institutes in France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
, Italy
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
, Japan
Japan
Japan is an island nation in East Asia. Located in the Pacific Ocean, it lies to the east of the Sea of Japan, China, North Korea, South Korea and Russia, stretching from the Sea of Okhotsk in the north to the East China Sea and Taiwan in the south...
and USA.
From 1984 Professor Feng changed his research field from elliptic equations to dynamical system
Dynamical system
A dynamical system is a concept in mathematics where a fixed rule describes the time dependence of a point in a geometrical space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, and the number of fish each springtime in a...
s such as Hamiltonian system
Hamiltonian system
In physics and classical mechanics, a Hamiltonian system is a physical system in which forces are momentum invariant. Hamiltonian systems are studied in Hamiltonian mechanics....
s and wave equation
Wave equation
The wave equation is an important second-order linear partial differential equation for the description of waves – as they occur in physics – such as sound waves, light waves and water waves. It arises in fields like acoustics, electromagnetics, and fluid dynamics...
s. He proposed symplectic algorithms for Hamiltonian systems based on symplectic geometry. Such algorithms can preserve the symplectic geometric structure of Hamiltonian systems.
He then led and supervised a research group on the symplectic algorithms for Hamiltonian systems with finite and infinite dimensions, and on dynamical systems with Lie algebra
Lie algebra
In mathematics, a Lie algebra is an algebraic structure whose main use is in studying geometric objects such as Lie groups and differentiable manifolds. Lie algebras were introduced to study the concept of infinitesimal transformations. The term "Lie algebra" was introduced by Hermann Weyl in the...
ic structures, such as contact systems, source-free systems, etc., making use of the corresponding geometry and the underlying Lie algebras and Lie groups. These algorithms are overwhelmingly superior to conventional algorithms in long term tracking and qualitative simulation in many practical applications, such as celestial mechanics
Celestial mechanics
Celestial mechanics is the branch of astronomy that deals with the motions of celestial objects. The field applies principles of physics, historically classical mechanics, to astronomical objects such as stars and planets to produce ephemeris data. Orbital mechanics is a subfield which focuses on...
, molecular dynamics
Molecular dynamics
Molecular dynamics is a computer simulation of physical movements of atoms and molecules. The atoms and molecules are allowed to interact for a period of time, giving a view of the motion of the atoms...
, etc.