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Personal profile

Quote

“If you look carefully, you can see PDEs everywhere.”

Research profile

Jan ten Thije Boonkkamp is an Associate Professor in the Department of Mathematics and Computer Science at Eindhoven University of Technology (TU/e). His research interests include:

* Numerical analysis - numerical methods for partial differential equations, finite volume methods for conservation laws, complete flux schemes, hyperbolic systems, time integration methods, Monge-Ampère equation, ray tracing

* Applied sciences: computational fluid dynamics, combustion theory, plasma physics, semiconductor simulation, computational illumination optics

Jan operates two main research lines

* Develop mathematical models for illumination optics, both analytical and numerical. An optical system is formulated as an optimal transport problem, subject to energy conservation. This approach allows us to derive a nonlinear PDE defining one of the optical surfaces. Efficient numerical solution methods for this equation are developed.

* Develop novel flux approximation schemes for conservation laws.

Basic idea is to compute the numerical flux from a local boundary value problem. The resulting numerical solution features properties of the exact solution

Academic background

Jan ten Thije Boonkkamp received his MSc from the Department of Applied Mathematics at the University of Twente in 1984. He then started working at the Centrum Wiskunde & Informatica, Amsterdam where he remained until 1988, when he joined Philips Research Laboratories in Eindhoven. In 1991, he joined TU/e. In January 2015, Jan was a Visiting Professor in the Department of Mathematics & Statistics, IIT Kanpur, India. Jan publishes regularly in leading journals, such as the Journal of Computational and Applied Mathematics, Journal of Computational Physics and Journal of Scientific Computing.

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Research Output 1985 2019

A least-squares method for a Monge-Ampère equation with non-quadratic cost function applied to optical design

Yadav, N. K., ten Thije Boonkkamp, J. H. M. & IJzerman, W. L., 1 Jan 2019, Numerical Mathematics and Advanced Applications ENUMATH 2017. Radu, F. A., Kumar, K., Berre, I., Nordbotten, J. M. & Pop, I. S. (eds.). Cham: Springer, p. 301-309 9 p. (Lecture Notes in Computational Science and Engineering; vol. 126)

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Monge-Ampère Equation
Optical design
Optical Design
Least Square Method
Cost functions

Complete flux scheme for parabolic singularly perturbed differential-difference equations

Kumar, S., Rathish Kumar, B. V. & ten Thije Boonkkamp, J. H. M., 1 Mar 2019, In : Numerical Methods for Partial Differential Equations. 35, 2, p. 790-804 15 p.

Research output: Contribution to journalArticleAcademicpeer-review

Differential-difference Equations
Difference equations
Singularly Perturbed
Fluxes
Parameter Perturbation
1 Citation (Scopus)

Computation of double freeform optical surfaces using a Monge–Ampère solver: Application to beam shaping

Yadav, N. K., ten Thije Boonkkamp, J. H. M. & IJzerman, W. L., 15 May 2019, In : Optics Communications. 439, p. 251-259 9 p.

Research output: Contribution to journalArticleAcademicpeer-review

Lenses
lenses
layouts
lens design
Wavefronts

Nonlinear flux approximation scheme for Burgers equation derived from a local BVP

ten Thije Boonkkamp, J. H. M., Kumar, N., Koren, B., van der Woude, D. A. M. & Linke, A., 2019, Numerical Mathematics and Advanced Applications ENUMATH 2017. Radu, F. A., Kumar, K., Berre, I., Nordbotten, J. M. & Pop, I. S. (eds.). Cham: Springer, p. 1015-1023 9 p. (Lecture Notes in Computational Science and Engineering; vol. 126)

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Approximation Scheme
Burgers Equation
Inviscid Limit
Iterative Solution
Two-point Boundary Value Problem

Solving inverse illumination problems with Liouville's equation

van Lith, B. S., ten Thije Boonkkamp, J. H. M. & IJzerman, W. L., 2019, Numerical Mathematics and Advanced Applications ENUMATH 2017. Radu, F. A., Kumar, K., Berre, I., Nordbotten, J. M. & Pop, I. S. (eds.). Cham: Springer, p. 311-319 9 p. (Lecture Notes in Computational Science and Engineering; vol. 126)

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Liouville equations
illumination
optics
control theory
optimal control

Courses

Analysis 1

1/09/12 → …

Course

Linear algebra 2

1/09/12 → …

Course

Professional portfolio

1/09/15 → …

Course

Student theses

Adaptive non-oscillatory complete flux schemes

Author: Wessels, F., 31 Aug 2015

Supervisor: ten Thije Boonkkamp, J. (Supervisor 1)

Student thesis: Master

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Analysis of a one-dimensional laminar flame

Author: Standaert, F., 30 Apr 1994

Supervisor: Mattheij, R. (Supervisor 1), Rienstra, S. (Supervisor 2) & ten Thije Boonkkamp, J. (Supervisor 2)

Student thesis: Master

Analysis of light mixing tubes using chaotic billiards theory

Author: Goorden, S., 31 Mar 2011

Supervisor: ten Thije Boonkkamp, J. (Supervisor 1) & Tukker, T. (Supervisor 2)

Student thesis: Master

File

Comparing two methods for Monte Carlo ray tracing

Author: van de Leur, L., 2013

Supervisor: ten Thije Boonkkamp, J. (Supervisor 1)

Student thesis: Bachelor

File

Complete flux scheme for compressible flow computation

Author: Marnah, N., 17 Dec 2010

Supervisor: ten Thije Boonkkamp, J. (Supervisor 1)

Student thesis: Master

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