Jan Mandel
Encyclopedia
Jan Mandel is a Czech
-American
mathematician
. He received his PhD from the Faculty of Mathematics and Physics, Charles University in Prague
and was a Senior Research Scientist there. Since 1986, he is professor of Mathematics
at the University of Colorado Denver
.
He has worked in the field of multigrid method
s and domain decomposition method
s. He developed the balancing domain decomposition
method and, with coauthors, published the convergence proofs of the FETI
, FETI-DP
, and BDDC
methods, and the proof of the equivalence of the FETI-DP
and the BDDC
methods. He has been involved in the field of dynamic data driven application system
s and data assimilation
with applications in wildfire
and epidemic
modeling
. He is the lead programmer of WRF-Fire
.
Czech Republic
The Czech Republic is a landlocked country in Central Europe. The country is bordered by Poland to the northeast, Slovakia to the east, Austria to the south, and Germany to the west and northwest....
-American
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
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....
. He received his PhD from the Faculty of Mathematics and Physics, Charles University in Prague
Charles University in Prague
Charles University in Prague is the oldest and largest university in the Czech Republic. Founded in 1348, it was the first university in Central Europe and is also considered the earliest German university...
and was a Senior Research Scientist there. Since 1986, he is professor of 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...
at the University of Colorado Denver
University of Colorado Denver
The University of Colorado Denver, shortened as CU Denver, UC Denver, or UCD, is a public university in the United States state of Colorado. It is one of three schools of the University of Colorado system. The university has two campuses — one in downtown Denver at the Auraria Campus, and the other...
.
He has worked in the field of multigrid method
Multigrid method
Multigrid methods in numerical analysis are a group of algorithms for solving differential equations using a hierarchy of discretizations. They are an example of a class of techniques called multiresolution methods, very useful in problems exhibiting multiple scales of behavior...
s and domain decomposition method
Domain decomposition method
In mathematics, the additive Schwarz method, named after Hermann Schwarz, solves a boundary value problem for a partial differential equation approximately by splitting it into boundary value problems on smaller domains and adding the results.- Overview :...
s. He developed the balancing domain decomposition
Balancing domain decomposition
In numerical analysis, the balancing domain decomposition method is an iterative method to find the solution of a symmetric positive definite system of linear algebraic equations arising from the finite element method . In each iteration, it combines the solution of local problems on...
method and, with coauthors, published the convergence proofs of the FETI
FETI
In mathematics, in particular numerical analysis, the FETI method is an iterative substructuring method for solving systems of linear equations from the finite element method for the solution of elliptic partial differential equations, in particular in computational mechanics In each iteration,...
, FETI-DP
FETI-DP
The FETI-DP method is a domain decomposition method that enforces equality of the solution at subdomain interfaces by Lagrange multipliers except at subdomain corners, which remain primal variables.The first mathematical analysis of the method was provided by Mandel and Tezaur...
, and BDDC
BDDC
In numerical analysis, BDDC is a domain decomposition method for solving large symmetric, positive definite systems of linear equations that arise from the finite element method. BDDC is used as a preconditioner to the conjugate gradient method...
methods, and the proof of the equivalence of the FETI-DP
FETI-DP
The FETI-DP method is a domain decomposition method that enforces equality of the solution at subdomain interfaces by Lagrange multipliers except at subdomain corners, which remain primal variables.The first mathematical analysis of the method was provided by Mandel and Tezaur...
and the BDDC
BDDC
In numerical analysis, BDDC is a domain decomposition method for solving large symmetric, positive definite systems of linear equations that arise from the finite element method. BDDC is used as a preconditioner to the conjugate gradient method...
methods. He has been involved in the field of dynamic data driven application system
Dynamic Data Driven Application System
A dynamic data driven application system is one where data is fed into an executing application either as the data is collected or from a data archive . The data will then be used to influence the measurements for additional data it may require. Current research for these systems focuses on...
s and data assimilation
Data assimilation
Applications of data assimilation arise in many fields of geosciences, perhaps most importantly in weather forecasting and hydrology. Data assimilation proceeds by analysis cycles...
with applications in wildfire
Wildfire modeling
In computational science, wildfire modeling is concerned with numerical simulation of wildland fires in order to understand and predict fire behavior. Wildfire modeling can ultimately aid wildland fire suppression, namely increase safety of firefighters and the public, reduce risk, and minimize...
and epidemic
Epidemic model
An Epidemic model is a simplified means of describing the transmission of communicable disease through individuals.-Introduction:The outbreak and spread of disease has been questioned and studied for many years...
modeling
Computer simulation
A computer simulation, a computer model, or a computational model is a computer program, or network of computers, that attempts to simulate an abstract model of a particular system...
. He is the lead programmer of WRF-Fire
WRF-Fire
WRF-Fire is a coupled atmosphere-wildfire model, which combines the Weather Research and Forecasting model with a fire spread model, implemented by the level set method....
.
External links
- Home page at University of Colorado Denver
- http://en.scientificcommons.org/jan_mandel
- http://www.thedenverchannel.com/health/19327133/detail.html (Interview with Mandel on ABC news)