Germund Dahlquist
Encyclopedia
Germund Dahlquist was a Swedish
mathematician
known primarily for his early contributions to the theory of numerical analysis
as applied to differential equation
s.
Dahlquist began to study mathematics at Stockholm University
in 1942 at the age of 17, where he cites the Danish mathematician Harald Bohr
(who was living in exile after the occupation of Denmark
during World War II
) as a profound influence.
He received the degree of licentiat
from Stockholm University in 1949, before taking a break from his studies to work at the Swedish Board of Computer Machinery (Matematikmaskinnämnden), working on (among other things) the early computer BESK
, Sweden's first. During this time, he also worked with Carl-Gustaf Rossby
on early numerical weather forecasts.
Dahlquist returned to Stockholm University to complete his Ph.D., “Stability and Error Bounds in the Numerical Solution of Ordinary Differential Equations", which he defended in 1958, with Fritz Carlson
and Lars Hörmander
as his advisors. As part of this work he introduced the logarithmic norm
(also introduced by Russian mathematician Sergei Lozinskii the same year).
In 1959 he moved to the Royal Institute of Technology
(KTH), where he would later establish what is now the Department of Numerical Analysis and Computer Science (NADA) in 1962, and become Sweden's first Professor of Numerical Analysis in 1963. He helped establish the Nordic journal of numerical analysis, BIT, in 1961. In 1965 he was elected into the Royal Swedish Academy of Engineering Sciences
(IVA).
The software package COMSOL Multiphysics
, for finite element analysis of partial differential equations, was started by a couple of Dahlquist's graduate students based upon codes developed for a graduate course at KTH.
Sweden
Sweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....
mathematician
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....
known primarily for his early contributions to the theory of numerical analysis
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
as applied to differential equation
Differential equation
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders...
s.
Dahlquist began to study mathematics at Stockholm University
Stockholm University
Stockholm University is a state university in Stockholm, Sweden. It has over 28,000 students at four faculties, making it one of the largest universities in Scandinavia. The institution is also frequently regarded as one of the top 100 universities in the world...
in 1942 at the age of 17, where he cites the Danish mathematician Harald Bohr
Harald Bohr
Harald August Bohr was a Danish mathematician and football player. After receiving his doctorate in 1910, Bohr became an eminent mathematician, founding the field of almost periodic functions. His brother was the Nobel Prize-winning physicist Niels Bohr...
(who was living in exile after the occupation of Denmark
Occupation of Denmark
Nazi Germany's occupation of Denmark began with Operation Weserübung on 9 April 1940, and lasted until German forces withdrew at the end of World War II following their surrender to the Allies on 5 May 1945. Contrary to the situation in other countries under German occupation, most Danish...
during World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
) as a profound influence.
He received the degree of licentiat
Licentiate
Licentiate is the title of a person who holds an academic degree called a licence. The term may derive from the Latin licentia docendi, meaning permission to teach. The term may also derive from the Latin licentia ad practicandum, which signified someone who held a certificate of competence to...
from Stockholm University in 1949, before taking a break from his studies to work at the Swedish Board of Computer Machinery (Matematikmaskinnämnden), working on (among other things) the early computer BESK
BESK
BESK was Sweden's first electronic computer, using vacuum tubes instead of relays. It was developed by Matematikmaskinnämnden and during a short time it was the fastest computer in the world. The computer was completed in 1953 and in use until 1966...
, Sweden's first. During this time, he also worked with Carl-Gustaf Rossby
Carl-Gustaf Rossby
Carl-Gustaf Arvid Rossby was a Swedish-U.S. meteorologist who first explained the large-scale motions of the atmosphere in terms of fluid mechanics....
on early numerical weather forecasts.
Dahlquist returned to Stockholm University to complete his Ph.D., “Stability and Error Bounds in the Numerical Solution of Ordinary Differential Equations", which he defended in 1958, with Fritz Carlson
Fritz Carlson
Fritz David Carlson was a Swedish mathematician. He's famous for* Carlson's theorem in complex analysis* Carlson's inequality*Carlson–Levin constant*Carlson theorem on Dirichlet series...
and Lars Hörmander
Lars Hörmander
Lars Valter Hörmander is a Swedish mathematician who has been called "the foremost contributor to the modern theory of linear partial differential equations". He was awarded the Fields Medal in 1962, and the Wolf Prize in 1988...
as his advisors. As part of this work he introduced the logarithmic norm
Logarithmic norm
In mathematics, the logarithmic norm is a real-valued functional on operators, and is derived from either an inner product, a vector norm, or its induced operator norm. The logarithmic norm was independently introduced by Germund Dahlquist and Sergei Lozinskiĭ in 1958, for square matrices. It has...
(also introduced by Russian mathematician Sergei Lozinskii the same year).
In 1959 he moved to the Royal Institute of Technology
Royal Institute of Technology
The Royal Institute of Technology is a university in Stockholm, Sweden. KTH was founded in 1827 as Sweden's first polytechnic and is one of Scandinavia's largest institutions of higher education in technology. KTH accounts for one-third of Sweden’s technical research and engineering education...
(KTH), where he would later establish what is now the Department of Numerical Analysis and Computer Science (NADA) in 1962, and become Sweden's first Professor of Numerical Analysis in 1963. He helped establish the Nordic journal of numerical analysis, BIT, in 1961. In 1965 he was elected into the Royal Swedish Academy of Engineering Sciences
Royal Swedish Academy of Engineering Sciences
The Royal Swedish Academy of Engineering Sciences or Kungl. Ingenjörsvetenskapsakademien , founded in 1919 by King Gustaf V, is one of the Royal Academies in Sweden...
(IVA).
The software package COMSOL Multiphysics
COMSOL Multiphysics
COMSOL Multiphysics is a finite element analysis, solver and Simulation software / FEA Software package for various physics and engineering applications, especially coupled phenomena, or multiphysics. COMSOL Multiphysics also offers an extensive interface to MATLAB and its toolboxes for a large...
, for finite element analysis of partial differential equations, was started by a couple of Dahlquist's graduate students based upon codes developed for a graduate course at KTH.
See also
- First and second Dahlquist barriers
Honors and awards
- SIAM 1988 John von Neumann lecturer.
- SIAM Germund Dahlquist Prize, established 1995, "Awarded to a young scientist (normally under 45) for original contributions to fields associated with Germund Dahlquist, especially the numerical solution of differential equations and numerical methods for scientific computing".
- Three honorary doctorates, from HamburgHamburg-History:The first historic name for the city was, according to Claudius Ptolemy's reports, Treva.But the city takes its modern name, Hamburg, from the first permanent building on the site, a castle whose construction was ordered by the Emperor Charlemagne in AD 808...
(1981), HelsinkiHelsinkiHelsinki is the capital and largest city in Finland. It is in the region of Uusimaa, located in southern Finland, on the shore of the Gulf of Finland, an arm of the Baltic Sea. The population of the city of Helsinki is , making it by far the most populous municipality in Finland. Helsinki is...
(1994), and LinköpingLinköping Institute of TechnologyThe Institute of Technology at Linköping University or Linköpings tekniska högskola is the faculty of science and engineering of Linköping University, located in Linköping and Norrköping in Sweden. Since its start in 1969 LiTH has had close ties with the Swedish transport and electronics industry...
(1996).