Research

My research interests include local defect correction (LDC), finite difference, finite volume and iterative methods and smoothed particle hydrodynamics (SPH).

I am currently working on finite volume methods for partial differential equations of diffusion/advection/reaction type together with Jan ten Thije Boonkkamp.

Our group also works on SPH, a meshless particle-based method that has been applied with great success in many fields in engineering and science. It is especially suited for treating problems with free surfaces, multiphase flow, high velocity impact, crack propagation and large deformations.

Selected publications

The following short list shows some of the publications that are representative for my work

1. • S.P. Korzilius, A.C.H. Kruisbrink, W.H.A. Schilders, M.J.H. Anthonissen and T. Yue.
   Momentum conserving methods that reduce clustering in SPH.
   

Technical Report CASA 14-15, Eindhoven University of Technology, Eindhoven, March 2014.

1. • J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen.
   The finite volume-complete flux scheme for advection-diffusion-reaction equations.
   Journal of Scientific Computing, 46(1), 47-70, 2011.
   

• R. Minero, M.J.H. Anthonissen, and R.M.M. Mattheij.

Solving parabolic problems using local defect correction in combination with the finite volume method.

Numerical Methods for Partial Differential Equations, Vol. 22, Issue 5, pages 1149-1172, September 2006.

• M. Sizov, M.J.H. Anthonissen, and R.M.M. Mattheij.

Analysis of the local defect correction and high order compact finite differences.

Numerical Methods for Partial Differential Equations, Vol. 22, Issue 4, pages 815-830, July 2006.

• R. Minero, M.J.H. Anthonissen, and R.M.M. Mattheij.

A local defect correction technique for time-dependent problems.

Numerical Methods for Partial Differential Equations, Vol. 22, Issue 1, pages 128-144, January 2006.

• M.J.H. Anthonissen, B.A.V. Bennett, and M.D. Smooke.

An adaptive multilevel local defect correction technique with application to combustion.

Combustion Theory and Modelling, Vol. 9, No. 2, pages 273-299, May 2005.

• M.J.H. Anthonissen, R.M.M. Mattheij, and J.H.M. ten Thije Boonkkamp.

Convergence analysis of the local defect correction method for diffusion equations.

Numerische Mathematik, 95(3):401-425, 2003.

• M.J.H. Anthonissen.

Local defect correction techniques: analysis and application to combustion.

PhD thesis, Eindhoven University of Technology, Eindhoven, 2001.

• M.J.H. Anthonissen, B. van 't Hof, and A.A. Reusken.

A finite volume scheme for solving elliptic boundary value problems on composite grids.

Computing, 61:285-305, 1998.

 

PhD students (co-promotor)

1. • Stan Korzilius.
   Second derivatives, particle collisions and travelling liquid slugs within smoothed particle hydrodynamics.
   PhD thesis, Eindhoven University of Technology, Eindhoven, 2016.
   

2. • Godwin Kakuba.
   

The boundary element method: errors and gridding for problems with hot spots.

PhD thesis, Eindhoven University of Technology, Eindhoven, 2011.

1. • Misha Sizov.
   Airfilm cooling through laser drilled holes.
   

PhD thesis, Eindhoven University of Technology, Eindhoven, 2007.

1. • Remo Minero.
   Local defect correction for time-dependent problems.
   PhD thesis, Eindhoven University of Technology, Eindhoven, 2006.
   
   

The long list of publications

This is a more extended list of publications that also includes preprints, papers in Dutch and articles in non-scientific journals.

1. • S.P. Korzilius, A.S. Tijsseling, Z. Bozkuş, M.J.H. Anthonissen, W.H.A. Schilders
   Modeling Liquid Slugs Accelerating in Inclined Conduits.
   ASME. J. Pressure Vessel Technol. 2017;139(6):061301-061301-10. doi:10.1115/1.4037716.
   

2. • R. Beltman, M.J.H. Anthonissen and B. Koren
   

Mimetic staggered discretization of incompressible Navier–Stokes for barycentric dual mesh.

In: C. Cances & P. Omnes (Eds.), Finite Volumes for Complex Applications VIII — Hyperbolic, Elliptic and Parabolic Problems (pp. 467-475). (Springer Proceedings in Mathematics & Statistics, No. 200), Dordrecht: Springer, 2017.

1. • J.H.M. ten Thije Boonkkamp, M.J.H. Anthonissen and R. Kwant
   

A two-dimensional complete flux scheme in local flow adapted coordinates.

In: C. Cancès & P. Omnes (Eds.), Finite Volumes for Complex Applications VIII — Hyperbolic, Elliptic and Parabolic Problems - FVCA8 2017 (pp. 437-445), (Springer Proceedings in Mathematics & Statistics, No. 200), Springer, 2017.

1. • F. Ischinger, M.J.H. Anthonissen and B. Koren.
   A monolithic fluid-structure interaction method, Application to a piston problem.
   

In: M. Papadrakakis, V. Papadopoulos, G. Stefanou, V. Plevris (Eds.), ECCOMAS Congress 2016, VII European Congress on Computational Methods in Applied Sciences and Engineering, Crete Island, Greece, 5–10 June 2016. 

1. • A.A. Sivas, M. Manguoğlu, J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen.
   

Discretization and parallel iterative schemes for advection-diffusion-reaction problems.

In: B. Karasözen, M. Manguoğlu, M. Tezer-Sezgin, S. Göktepe, Ö. Uğur (Eds.), Numerical Mathematics and Advanced Applications 2015 (Proceedings of ENUMATH 2015, the European Conference on Numerical Mathematics and Advanced Applications, Ankara, Turkey, September 14-18, 2015), Springer International Publishing, 2016.

1. • S.P. Korzilius, W.H.A. Schilders and M.J.H. Anthonissen.
   An improved CSPM approximation for multi-dimensional second-order derivatives.
   Technical Report CASA 15-18, Eindhoven University of Technology, Eindhoven, April 2015.
   

2. • G. Kakuba and M.J.H. Anthonissen.
   Local defect correction for boundary integral equation methods.
   Computer Modeling in Engineering and Sciences, 99(6), 445-462, 2014.
   

3. • M.J.H. Anthonissen and J.H.M. ten Thije Boonkkamp.
   

The complete flux scheme in cylindrical coordinates.

In: J. Fuhrmann, M. Ohlberger & C. Rohde (Eds.), Conference Paper: Finite Volumes for Complex Applications VII - Methods and Theoretical Aspects (FVCA 7, Berlin, Germany, June 2014), (Springer Proceedings in Mathematics & Statistics, 77, pp. 77-85). Berlin: Springer. 2014.

1. • J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen.
   

Numerical dissipation and dispersion of the homogeneous and complete flux schemes.

In: J. Fuhrmann, M. Ohlberger & C. Rohde (Eds.), Conference Paper: Finite Volumes for Complex Applications VII - Methods and Theoretical Aspects (FVCA 7, Berlin, Germany, June 2014), (Springer Proceedings in Mathematics & Statistics, 77, pp. 117-125). Heidelberg: Springer. 2014.

1. • S.P. Korzilius, A.C.H. Kruisbrink, T. Yue, W.H.A. Schilders and M.J.H. Anthonissen.
   

Momentum conserving methods that reduce particle clustering in SPH.

In: D. Violeau, A. Hérault & A. Joly (Eds.), Conference Paper: 9th International Smoothed Particle Hydrodynamics European Research Interest Community Workshop (SPHERIC 2014, Paris, France, June 3-5, 2014, (pp. 268-275). Roma: INSEAN. 2014.

1. • S.P. Korzilius, A.C.H. Kruisbrink, W.H.A. Schilders, M.J.H. Anthonissen and T. Yue.
   Momentum conserving methods that reduce clustering in SPH.
   

Technical Report CASA 14-15, Eindhoven University of Technology, Eindhoven, March 2014.

1. • M.J.H. Anthonissen and J.H.M. ten Thije Boonkkamp.
   The complete flux scheme in cylindrical coordinates.
   Technical Report CASA 14-06, Eindhoven University of Technology, Eindhoven, March 2014.
   

2. • J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen.
   Numerical dissipation and dispersion of the homogeneous and complete flux schemes.
   Technical Report CASA 14-04, Eindhoven University of Technology, Eindhoven, March 2014.
   

3. • S.P. Korzilius, W.H.A. Schilders and M.J.H. Anthonissen.
   An improved corrective smoothed particle method approximation for second‐order derivatives.
   Conference Paper: 8th International Smoothed Particle Hydrodynamics European Research Interest Community Workshop (SPHERIC 2013, Trondheim, Norway, June 4-6, 2013), pp. 41-46, 2013.
   

4. • G. Kakuba and M.J.H. Anthonissen.
   

Local defect correction for boundary integral equation methods.

Technical Report CASA 13-10, Eindhoven University of Technology, Eindhoven, May 2013.

1. • S.P. Korzilius, W.H.A. Schilders and M.J.H. Anthonissen.
   

An improved corrective smoothed particle method approximation for second-order derivatives.

Technical Report CASA 13-06, Eindhoven University of Technology, Eindhoven, April 2013.

1. • C.J.J. Vleugels, A. Muntean, M.J.H. Anthonissen and T.I. Seidman.
   Minimizing driver's irritation at a roadblock.
   Technical Report CASA 13-01, Eindhoven University of Technology, Eindhoven, January 2013.
   

2. • J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen.
   The Complete Flux Scheme for Conservation Laws in Curvilinear Coordinates.
   In: Finite Volume Method - Powerful Means of Engineering Design, PhD. Radostina Petrova (Ed.), ISBN: 978-953-51-0445-2, InTech, 2012.
   

3. • T. Aiki, M.J.H. Anthonissen and A. Muntean.
   On a one-dimensional shape-memory alloy model in its fast-temperature-activation limit.
   Discrete and Continuous Dynamical Systems - Series S, 5(1), 15-28, 2012.
   

4. • J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen.
   The finite volume-complete flux scheme for advection-diffusion-reaction equations.
   Journal of Scientific Computing, 46(1), 47-70, 2011.
   

5. • S.A. Goorden, S.P. Korzilius, J.H.M. ten Thije Boonkkamp, M.J.H. Anthonissen and B.V. Rathish Kumar.
   NPZ-model with seasonal variability of plankton population dynamics.
   Applied Mathematical and Computational Sciences, 3(2), 227-248, 2011.
   

6. • J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen.
   

Extension of the complete flux scheme to time-dependent conservation laws.

In G. Kreiss, P. Lötstedt, A. Malqvist & M. Neytcheva (Eds.), Numerical Mathematics and Advanced Applications 2009 (Proceedings of ENUMATH 2009, the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, Sweden, June 29-July 3, 2009), pp. 865-873, Berlin, Springer, 2010.

1. • J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen.
   The finite volume-complete flux scheme for advection-diffusion-reaction equations.
   Technical Report CASA 10-07, Eindhoven University of Technology, Eindhoven, January 2010.
   

2. • J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen.
   Extension of the complete flux scheme to time-dependent conservation laws.
   Technical Report CASA 09-32, Eindhoven University of Technology, Eindhoven, September 2009.
   

3. • M.J.H. Anthonissen and J.H.M. ten Thije Boonkkamp.
   A compact high order finite volume scheme for advection-diffusion-reaction equations.
   

In: Theodore E. Simos, George Psihoyios, Ch. Tsitouras (Eds.), Numerical analysis and applied mathematics (Proceedings International Conference on Numerical analysis and Applied Mathematics, Rethymno, Crete, Grece, September 18-22, 2009), Volume 1 (AIP Conference Proceedings 1168, pp. 410-414). American Institute of Physics, Melville, New York, 2009.

1. • M.J.H. Anthonissen and J.H.M. ten Thije Boonkkamp.
   A compact high order finite volume scheme for advection-diffusion-reaction equations.
   Technical Report CASA 09-24, Eindhoven University of Technology, Eindhoven, August 2009.
   

2. • M.J.H. Anthonissen (editor).
   Liber amicorum Hennie ter Morsche.
   Eindhoven University of Technology, Eindhoven, 2009.
   

3. • T. Aiki, M.J.H. Anthonissen, A. Muntean.
   On a one-dimensional shape-memory alloy model in its fast-temperature-activation limit.
   Technical Report CASA 09-22, Eindhoven University of Technology, Eindhoven, June 2009.
   

4. • J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen.
   A novel flux approximation scheme for spherically symmetric conservation laws.
   International Journal of Pure and Applied Mathematics, 53, No. 2, 175-18, 2009.
   

5. • J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen.
   The complete flux scheme for spherically symmetric conservation laws.
   

In: M. Bubak, G.D. van Albada, J. Dongarra, P.M.A. Sloot (Eds.), Computational Science - ICCS 2008 (Proceedings 8th International Conference, Kraków, Poland, June 23-25, 2008), Volume I. (Lecture Notes in Computer Science, Vol. 5101, pp. 651-660). Springer, Berlin, 2008.

1. • J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen.
   The finite volume-complete flux scheme for one-dimensional advection-diffusion-reaction equations.
   Technical Report CASA 08-28, Eindhoven University of Technology, Eindhoven, September 2008.
   

2. • J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen.
   The complete flux scheme for spherically symmetric conservation laws.
   Technical Report CASA 08-08, Eindhoven University of Technology, Eindhoven, March 2008.
   

• M.J.H. Anthonissen.

Local defect correction in numerical simulation of surface remelting.

International Journal of Computer Mathematics, Vol. 84, Issue 2, pages 251-259, February 2007.

• G. Kakuba, R.M.M. Mattheij and M.J.H. Anthonissen.

Local defect correction for the boundary element method.

CMES: Computer Modeling in Engineering & Sciences, Vol. 15, No. 3, pp. 127-136, 2006.

• R. Minero, M.J.H. Anthonissen, and R.M.M. Mattheij.

Solving parabolic problems using local defect correction in combination with the finite volume method.

Numerical Methods for Partial Differential Equations, Vol. 22, Issue 5, pages 1149-1172, September 2006.

• M. Sizov, M.J.H. Anthonissen, and R.M.M. Mattheij.

Analysis of the local defect correction and high order compact finite differences.

Numerical Methods for Partial Differential Equations, Vol. 22, Issue 4, pages 815-830, July 2006.

• G. Kakuba, R.M.M. Mattheij and M.J.H. Anthonissen.

Local defect correction for the boundary element method.

Technical Report CASA 06-18, Eindhoven University of Technology, Eindhoven, 2006.

• M.J.H. Anthonissen.

Local defect correction in numerical simulation of surface remelting.

Technical Report CASA 06-01, Eindhoven University of Technology, Eindhoven, January 2006.

• R. Minero, M.J.H. Anthonissen, and R.M.M. Mattheij.

A local defect correction technique for time-dependent problems.

Numerical Methods for Partial Differential Equations, Vol. 22, Issue 1, pages 128-144, January 2006.

• M.J.H. Anthonissen, D. Hömberg, and W. Weiss.

Real-Time Control of Surface Hardening.

Progress in Industrial Mathematics at ECMI 2004. Mathematics in Industry, Vol. 8, pages 356-360. Di Bucchianico, A.; Mattheij, R.M.M.; Peletier, M.A. (eds.). Springer, Berlin, 2006.

• R. Minero, H.G. ter Morsche and M.J.H. Anthonissen.

Convergence properties of the local defect correction method for parabolic problems.

Technical Report CASA 05-40, Eindhoven University of Technology, Eindhoven, October 2005.

• M.J.H. Anthonissen and R. Minero.

Conditions for one-step convergence of the local defect correction method for elliptic problems.

Technical Report CASA 05-39, Eindhoven University of Technology, Eindhoven, October 2005.

• M.J.H. Anthonissen.

Local grid refinement in numerical simulation of laser surface remelting.

Proceedings of the joint DCABES and ICPACE Meeting.

Craig A., Lai C.-H., Pericleous, K.A. (Eds.). CMS Press, University of Greenwich, UK. August 2005.

• R. Minero, M.J.H. Anthonissen, and R.M.M. Mattheij.

Solving parabolic problems using local defect correction in combination with the finite volume method.

Technical Report CASA 05-27, Eindhoven University of Technology, Eindhoven, June 2005.

• R. Minero, M.J.H. Anthonissen, and R.M.M. Mattheij.

Local defect correction for time-dependent partial differential equations.

Technical Report CASA 05-17, Eindhoven University of Technology, Eindhoven, April 2005.

• M.J.H. Anthonissen, B.A.V. Bennett, and M.D. Smooke.

An adaptive multilevel local defect correction technique with application to combustion.

Combustion Theory and Modelling, Vol. 9, No. 2, pages 273-299, May 2005.

• M.J.H. Anthonissen.

Local defect correction techniques applied to a combustion problem.

Lecture Notes in Computational Science and Engineering. Vol. 40, pages 185-192. Kornhuber, R.; Hoppe, R.; Périaux, J.; Pironneau, O.; Widlund, O.; Xu, J. (Eds.), 2004. (Proceedings of the 15th International Conference on Domain Decomposition Methods in Berlin, Germany)

• M. Sizov, M.J.H. Anthonissen, R.M.M. Mattheij.

Analysis of the local defect correction and high order compact finite differences.

Technical Report RANA 04-29, Eindhoven University of Technology, Eindhoven, November 2004.

• R. Minero, M.J.H. Anthonissen, and R.M.M. Mattheij.

A local defect correction technique for time-dependent problems.

Technical Report RANA 04-25, Eindhoven University of Technology, Eindhoven, October 2004.

• M.J.H. Anthonissen.

Glas

Supremum, 36-4:22-24, Augustus 2004.

In Dutch.

• I.E.M. Severens, M.J.H. Anthonissen, R.M.M. Mattheij, J.M.L. Maubach.

Application of the local defect correction method in discrete element method simulations.

Technical Report RANA 04-17, Eindhoven University of Technology, Eindhoven, August 2004.

• M. Sizov, M.J.H. Anthonissen, and R.M.M. Mattheij.

Analysis of the convergence behaviour of the local defect correction method for one dimensional convection-diffusion problems.

Technical Report RANA 04-11, Eindhoven University of Technology, Eindhoven, April 2004.

• M.J.H. Anthonissen.

Local defect correction techniques applied to a combustion problem.

Technical Report RANA 03-30, Eindhoven University of Technology, Eindhoven, December 2003.

• Martijn Anthonissen, Debby Lanser.

Gerard van Oortmerssen, manager van toegepast onderzoek.

ITW Nieuws, 12-2:11-14, November 2003.

In Dutch.

• Martijn Anthonissen.

Het wiskundeonderwijs aan de technische universiteiten.

ITW Nieuws, 12-2:15-16, November 2003.

In Dutch.

• M.J.H. Anthonissen, B.A.V. Bennett, and M.D. Smooke.

An adaptive multilevel local defect correction technique with application to combustion.

Technical Report RANA 03-24, Eindhoven University of Technology, Eindhoven, October 2003.

• M.J.H. Anthonissen, R.M.M. Mattheij, and J.H.M. ten Thije Boonkkamp.

Convergence analysis of the local defect correction method for diffusion equations.

Numerische Mathematik, 95(3):401-425, 2003.

• Martijn Anthonissen.

MetaPost: Mooie plaatjes in LaTeX.

ITW Nieuws, 12-1:19-22, June 2003.

In Dutch.

1. •M.J.H. Anthonissen (editor).
   

Liber amicorum Jos Jansen.

Eindhoven University of Technology, Eindhoven, 2001.

• M.J.H. Anthonissen.

Local defect correction techniques: analysis and application to combustion.

PhD thesis, Eindhoven University of Technology, Eindhoven, 2001. 

• M.J.H. Anthonissen, R.M.M. Mattheij, and J.H.M. ten Thije Boonkkamp.

Convergence results for the local defect correction method as an iterative process.

Technical Report RANA 00-14, Eindhoven University of Technology, Eindhoven, June 2000.

• M.J.H. Anthonissen, B. van 't Hof, and A.A. Reusken.

An iterative finite volume discretization method for solving elliptic boundary value problems on locally refined grids.

Nieuw Archief voor Wiskunde, 17:111-123, 1999.

• M.J.H. Anthonissen, B. van 't Hof, and A.A. Reusken.

A finite volume scheme for solving elliptic boundary value problems on composite grids.

Computing, 61:285-305, 1998.

• M. Anthonissen, B. van 't Hof, and A. Reusken.

A finite volume scheme for solving elliptic boundary value problems on composite grids.

Technical Report Bericht Nr. 152, Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Aachen, February 1998.

• M.J.H. Anthonissen, B. van 't Hof, and A.A. Reusken.

A finite volume scheme for solving elliptic boundary value problems on composite grids.

Technical Report RANA 98-04, Eindhoven University of Technology, Eindhoven, February 1998.

• M.J.H. Anthonissen and J. de Graaf.

Hopper's shape evolution equation.

Technical Report Textos de Matemática, Série B, Nr. 20, Universidade de Coimbra, Coimbra, Portugal, 1999.

• M.J.H. Anthonissen.

Plane stokes flow with a free boundary driven solely by surface tension.

Technical Report RANA 99-08, Eindhoven University of Technology, Eindhoven, February 1999.

• J. Boersma and M.J.H. Anthonissen.

Calculations in mathematica on low-frequency diffraction by a circular disk.

Applied Computational Electromagnetics Society Journal, 11(1):47-56, 1996.

• M.J.H. Anthonissen and J. Boersma.

Calculations in mathematica on low-frequency diffraction by a circular disk.

Technical Report EUT 95-WSK-01, Eindhoven University of Technology, Eindhoven, December 1995.

• M.J.H. Anthonissen.

Plane stokes flow with a free boundary driven solely by surface tension.

Master's thesis, Eindhoven University of Technology, Eindhoven, 1995.