Anders Szepessy (born 1960) is a Swedish mathematician.
Szepessy received his PhD in 1989 from Chalmers University of Technology with thesis Convergence of the streamline diffusion finite element method for conservation laws under the supervision of Claes Johnson. [1] [2] Szepessy is now a professor of mathematics and numerical analysis at KTH Royal Institute of Technology. [3]
His research area is applied mathematics, especially partial differential equations. [3]
Szepessy was an invited speaker at the International Congress of Mathematicians in 2006 in Madrid. [4] He was elected a member of the Royal Swedish Academy of Sciences in 2007.
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed analytical or empirical analysis of a particular problem can be used for comparison. A final validation is often performed using full-scale testing, such as flight tests.
Burgers' equation or Bateman–Burgers equation is a fundamental partial differential equation and convection–diffusion equation occurring in various areas of applied mathematics, such as fluid mechanics, nonlinear acoustics, gas dynamics, and traffic flow. The equation was first introduced by Harry Bateman in 1915 and later studied by Johannes Martinus Burgers in 1948.
Numerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs).
High-resolution schemes are used in the numerical solution of partial differential equations where high accuracy is required in the presence of shocks or discontinuities. They have the following properties:
Lloyd Nicholas Trefethen is an American mathematician, professor of numerical analysis and head of the Numerical Analysis Group at the Mathematical Institute, University of Oxford.
Bram van Leer is Arthur B. Modine Emeritus Professor of aerospace engineering at the University of Michigan, in Ann Arbor. He specializes in Computational fluid dynamics (CFD), fluid dynamics, and numerical analysis. His most influential work lies in CFD, a field he helped modernize from 1970 onwards. An appraisal of his early work has been given by C. Hirsch (1979)
In numerical analysis, Broyden's method is a quasi-Newton method for finding roots in k variables. It was originally described by C. G. Broyden in 1965.
Finite element exterior calculus (FEEC) is a mathematical framework that formulates finite element methods using chain complexes. Its main application has been a comprehensive theory for finite element methods in computational electromagnetism, computational solid and fluid mechanics. FEEC was developed in the early 2000s by Douglas N. Arnold, Richard S. Falk and Ragnar Winther, among others. Finite element exterior calculus is sometimes called as an example of a compatible discretization technique, and bears similarities with discrete exterior calculus, although they are distinct theories.
Roland Glowinski was a French-American mathematician. He obtained his PhD in 1970 from Jacques-Louis Lions and was known for his work in applied mathematics, in particular numerical solution and applications of partial differential equations and variational inequalities. He was a member of the French Academy of Sciences and held an endowed chair at the University of Houston from 1985. Glowinski wrote many books on the subject of mathematics. In 2012, he became a fellow of the American Mathematical Society.
Randall J. LeVeque is a Professor of Applied Mathematics at University of Washington who works in many fields including numerical analysis, computational fluid dynamics, and mathematical theory of conservation laws. Among other contributions, he is lead developer of the open source software project Clawpack for solving hyperbolic partial differential equations using the finite volume method. With Zhilin Li, he has also devised a numerical technique called the immersed interface method for solving problems with elastic boundaries or surface tension.
In mathematics and physics, homogenization is a method of studying partial differential equations with rapidly oscillating coefficients, such as
Burton Wendroff is an American applied mathematician known for his contributions to the development of numerical methods for the solution of hyperbolic partial differential equations. The Lax–Wendroff method for the solution of hyperbolic PDE is named for Wendroff.
István Gyöngy is a Hungarian mathematician working in the fields of stochastic differential equations, stochastic partial differential equations and their applications to nonlinear filtering and stochastic control. Recently, he has focused his attention on numerical analysis and especially accelerated numerical methods, making use of Richardson extrapolation.
False diffusion is a type of error observed when the upwind scheme is used to approximate the convection term in convection–diffusion equations. The more accurate central difference scheme can be used for the convection term, but for grids with cell Peclet number more than 2, the central difference scheme is unstable and the simpler upwind scheme is often used. The resulting error from the upwind differencing scheme has a diffusion-like appearance in two- or three-dimensional co-ordinate systems and is referred as "false diffusion". False-diffusion errors in numerical solutions of convection-diffusion problems, in two- and three-dimensions, arise from the numerical approximations of the convection term in the conservation equations. Over the past 20 years many numerical techniques have been developed to solve convection-diffusion equations and none are problem-free, but false diffusion is one of the most serious problems and a major topic of controversy and confusion among numerical analysts.
The following is a timeline of numerical analysis after 1945, and deals with developments after the invention of the modern electronic computer, which began during Second World War. For a fuller history of the subject before this period, see timeline and history of mathematics.
Annalisa Buffa is an Italian mathematician, specializing in numerical analysis and partial differential equations (PDE). She is a professor of mathematics at EPFL and hold the Chair of Numerical Modeling and Simulation.
Tai-Ping Liu is a Taiwanese mathematician, specializing in partial differential equations.
Tang Tao is a Chinese mathematician currently serving as President of BNU-HKBU United International College. Tang is a member of the Chinese Academy of Sciences. He is a fellow of the Society for Industrial and Applied Mathematics and American Mathematical Society.
Christoph Schwab is a German applied mathematician, specializing in numerical analysis of partial differential equations and boundary integral equations.
James Thomas Beale is an American mathematician, specializing in fluid dynamics, partial differential equations, and numerical analysis.