Fred Vermolen

I am involved in analysis and numerical methods for partial differential equations. Furthermore, I am interested in the quantification of uncertainty, as well as in probabilistic models. I am mostly involved in biology-and physics inspired applications.

We are organizing a Summer School on (Bulk-)Surface Partial Differential Equations at UHasselt, June 26 -- 29, 2023

Solving partial differential equations (PDEs) is crucially important in many disciplines within science, engineering and even in economics. Next to these disciplines, more and more biological processes are simulated using PDE-based frameworks. Examples are contraction of skin that develops after a serious burn injury, or the simulation of pattern formation of the skin of zebrafish or tigers. Even on the smallest units of life, e.g. cells, PDEs are solved to simulate processes like cell migration, and the impact that cells inflict on their immediate environment. This impact may be caused by chemicals that are released by cells, or by forces that are exerted on their environment during migration. PDEs often occur as conservation laws for energy, momentum or mass in body-like structures. Next to solving PDEs in bulks, PDEs may also govern on very thin shells or layers inside the bulk or surrounding the bulk. If the thickness of the layer is much smaller than the dimensions of the bulk, then one typically neglects the thickness and treats the layer as a surface within the bulk or around the bulk, that is, the surface has zero measure in the body. In various applications, this layer may separate two different regimes or phases. In these cases, the layer is commonly referred to as an interface, and this interface may move within the domain of computation over time. Various numerical approaches exist to deal with such moving interfaces. In this summer school, we treat the phase field method as one of the most-widely used methods to deal with moving interfaces. In many applications, the (interfacial) surface may, furthermore, be subject to diffusional transport over the surface, which results into a PDE over the surface. The resulting Surface PDEs (SPDEs) are composed by gradient and divergence operators, as well as Laplace-Beltrami operators over the surface. The numerical solutions to SPDEs can help predicting relevant results that are difficult or impossible to forecast on the basis of experiments. Often the solutions over the surface PDE is directly coupled to the solution of bulk PDE.

In this summer school, we focus on numerical (predominantly finite element) strategies applied to (bulk-)surface PDEs and phase-field problems. The finite element method is based on variational principles and allows a large degree of geometrical flexibility and flexibility regarding possible jumps of material constants. The summer school will focus on implementation and development of bulk-surface (finite element) discretizations. The goal of this summer school is to give the participants an introduction to the (bulk-)surface finite element and other discretization methods for phase field problems. The course will be centered around the following elements:

- Understanding the core definition of the polynomial (Lagrangian) finite element spaces;

- Understanding the gradient, divergence and Laplace-Beltrami differential operators on manifolds;

- Understanding and implementing a (bulk-)surface method for a proto-problem;

- Understanding and implementing finite difference methods for phase-field problems;

- Some aspects from today’s state-of-the-art research in (moving) (bulk-)surface problems.

The summer school will therefore be amenable to (applied) mathematicians, engineers and scientists. The summer school will be open to participants having a basic knowledge of calculus and partial differential equations as they are taught to engineers and scientists. All sessions will be hands-on, meaning that sufficient time for exercises and their discussion is planned. Lecturers will be experts in the field: **Anotida Madzvamuse (University of British Columbia, Canada), Chandrasekhar Venkataraman (University of Sussex, UK), Davide Cuseddu (University of Lisbon, Portugal), Massimo Fritelli (University of Salento, Italy) and Sebastian Aland (University of Freiberg, Germany)**.

The duration of the summer school is four days. Each day will be divided in a theoretical session in the morning, which is followed by hands-on assignments in the afternoon.

Day 1.

Lecture: Basic notions of finite element methods (weak form, Galerkin method, Basis functions), introduction into surface PDEs

Lab work: Matlab session to write bulk finite element code in 2D (3D)

Day 2.

Lecture: Continuation of surface PDEs, Basic notions of surface finite element methods (weak form), method of lines (time integration)

Lab work: Matlab session to write surface finite element code in 2D (3D)

Day 3.

Lecture: Bulk-surface finite elements, treatment of moving surface element methods

Lab work: Fenics project for time-dependent bulk-surface finite elements (application) in 2D (3D)

Day 4.

Lecture: Introduction to Phase-field methods for moving interface problems

Lab work: finite differences for phase-field methods

**Publications**

J. Lu, F.J. Vermolen. A spatial Markov Chain cellular automata model for the spread of viruses. In: Tavares, J.M.R.S. et al. Lecture Notes in Computational Vision and Biomechanics, Springer, Cham, 112-122 (2023)

Q. Peng, F.J. Vermolen, D. Weihs. Predicting the efficacy of stalk cells following leading cells through a micro-channel using morphoelasticity and a cell shape evolution model. In: Tavares, J.M.R.S. et al. Lecture Notes in Computational Vision and Biomechanics, Springer, Cham, 112-122 (2023)

P.P.M. van Zuijlen, H.I. Korkmaz, V.M. Sheraton, T.M. Haanstra, A. Pijpe, A. de Vries, C.H. van der Vlies, E. Bosma, E. de Jong, E. Middelkoop, F.J. Vermolen, P.M.A. Sloot. The future of burn care from a complexity science perspective. Journal of Burn Care and Research, 43 (6), 1312-1321 (2022)

G. Egberts, A. Desmoulieres, F.J. Vermolen, P.P.M. van Zuijlen. Sensitivity of a two-dimensional biomorphoelastic model for post-burn contraction. Biomechanics and Modelling in Mechanobiology, https://doi.org/10.1007/s10237-022-01634-w (2022)

Q. Peng, F.J. Vermolen. Numerical methods to compute stresses and displacements from cellular forces: Application to the contraction of tissue. Journal of Applied and Computational Mathematics, 404, 113892 (2022)

Q. Peng, W.S. Gorter, F.J. Vermolen. Comparison between a phenomenological approach and a morphoelasticity approach regarding the displacement of extracellular matrix. Biomechanics and Modelling in Mechanobiology, 21, 919-935 (2022)

H.I Korkmaz, F.B. Niessen, A. Pijpe, V.M. Sheraton, F.J. Vermolen, P.A.J. Krijnen, H.W.M. Niessen, P.M.A. Sloot, E. Middelkoop, S. Gibbs, P.P.M. van Zuijlen. Scar formation from the perspective of complexity science: a new look at the biological system as a whole. Journal of Wound Care, 31 (2), 178-184 (2022)

G. Egberts, M. Schaaphok, F.J. Vermolen, P.P.M. van Zuijlen. A Bayesian finite-element trained machine learning approach for predicting post-burn contraction. Neural Computing and Applications, 34, 8635-8642 (2022)

Q. Peng, F.J. Vermolen. Upscaling between an agent-based model (smoothed particle approach) and a continuum-based model for skin contraction. Journal of Mathematical Biology, 85 (3), 1-27 (2022)

Q. Peng, F.J. Vermolen. Point forces in elasticity equation and their alternatives in multi dimensions. Mathematics and Computers in Simulation, 199, 182-201 (2022)

Q. Peng, F.J. Vermolen, D. Weihs. Physical confinement and cell proximity increase cell migration rates and invasiveness: A mathematical model for cancer cell invasion through flexible channels. arXiv preprint, arXiv:2208.10934 (2022)

F.J. Vermolen, D.R. den Bakker, C. Vuik. On the fundamental solutions-based inversion of Laplace

matrices. Results in Applied Mathematics, 15, https://www.sciencedirect.com/science/article/pii/S2590037422000292?via%3DiHub (2022)

G. Egberts, F.J. Vermolen, P.P.M. van Zuijlen. Stability of a one-dimensional morphoelastic model for post-burn contraction. Journal of Mathematical Biology, 83 (3), 1-35 (2021)

G. Egberts, F.J. Vermolen, P.P.M. van Zuijlen. Sensitivity and feasibility of a one-dimensional morphoelastic model for post-burn contraction. Biomechanics and Mechanics in Mechanobiology, https://doi.org/10.1007/s10237-021-01499-5 (2021)

Q. Peng, F.J. Vermolen, D. Weihs. A formalism for modelling traction forces and cell shape evolution during cell migration in various biomedical processes. Biomechanics and Modelling in Mechanobiology, 20, 1459-1475 (2021), https://doi.org/10.1007/s10237-021-01456-2

G. Egberts, D. Smits, F.J. Vermolen, P.P.M. van Zuijlen. Some mathematical properties of morphoelasticity. In: European Numerial Mathematics and Advanced Applications Conference (ENUMATH 2019), Springer, 119-1127 (2021)

F.J. Vermolen, C. Rodrigo, F. Gaspar, K. Kumar. Computational mathematics aspects of flow and mechanics of porous media; State-of-the-art computational methods in the mechanics and flow. Computational Geosciences, 25(2), 601-602 (2021)

J. Chen, D. Weihs, F.J. Vermolen. A cellular automata model of oncolytic virotherapy in pancreatic cancer. Bulletin of Mathematical Biology. 82 (8), 1-25 (2020)

M. Rahrah, F.J. Vermolen. A moving finite element framework for fast infiltration in nonlinear poroelastic media. Computational Geosciences. accepted (2020), https://doi.org/10.1007/s10596-020-09959-0

M. Rahrah, L.A. Lopez-Pena, F.J. Vermolen, B.J. Meulenbroek. Network-inspired versus Kozeny-Carman permeability-porosity relations applied to Biot's poroelasticity model. Journal of Industrial Mathematics. **10, **19 (2020). https://doi.org/10.1186/s13362-020-00087-z

Q. Peng, F.J. Vermolen. Agent-Based Modelling and Parameter Sensitivity Analysis with a Finite-Element Method for Skin Contraction. Biomechanics and Modelling in Mechanobiology (2020), 19 (6), 2525-2551, https://doi.org/10.1007/s10237-020-01354-z

F.J. Vermolen. A spatial Markov Chain Cellular Automata Model for the Spread of Viruses. arXiv preprint. arXiv:2004.05635 (2020)

F.J. Vermolen. Mathematical modeling of healing of burns. In: Innovations and emerging Technologies in wound care. Chapter 1: 1 --20 (2020)

F.J. Vermolen, I. Pölönen. Uncertainty quantification on a Markov-chain model for the progression of skin cancer. Journal of Mathematical Biology. 80(3), 545--573 (2020)

J. Chen, D. Weihs, F.J. Vermolen. Computational modelling of therapy on pancreatic cancer in its early stages. Biomechanics and Modelling in Mechanobiology. 19, 427--444 (2020)

F.J. Vermolen, P.P. van Zuijlen. Can mathematics and computational modelling help treat deep tissue injuries? Advances in wound care. 8(12), 703--714 (2019)

J. Hinz, J. van Zwieten, M. Möller, F.J. Vermolen. Isogeometric analysis of the Gray-Scott reaction-diffusion equations for pattern formation on evolving surfaces and applications to human gyrofication. arXiv preprint. arXiv:1910.12588 (2019)

L.A. Lopez-Pena, B. Meulenbroek, F.J. Vermolen. A network model for the biofilm growth in porous media and its effects on permeability and porosity. Computing and Visualisation in Science. 21(1--6), 11--22 (2019)

M. Rahrah, F.J. Vermolen, L.A. Lopez-Pena, B.J. Meulenbroek. A poroelasticity model using a networlk-inspired porosity-permeability relation. In: Fargo I., Simon P. (eds) Progress in industrial mathematics at ECMI 2018. Mathematics in Industry, vol 30 Springer, Cham (2019)

J. Chen, D. Weihs, F.J. Vermolen. Computational cell-based modelling and visualisation of cancer development and progression. In: Tavares J., Fernandes P. (eds) New developments on computational methods and imaging in biomechanics and biomedical engineering. Lecture notes in computational vision and biomechanics, vol 33. Springer, Cham (2019)

L.A. Lopez-Pena, B.J. Meulenbroek, F.J. Vermolen. Conditions for upscalability of bioclogging in pore network models. Computational Geosciences. 22(6), 1543--1559 (2018)

J. Chen, D. Weihs, M. van Dijk, F.J. Vermolen. A phenomenological model for cell and nucleus deformation during cancer metastasis. Biomechanics and Modelling in Mechanobiology. 17(5), 1429--1450 (2018)

M. Rahrah, F.J. Vermolen. Monte Carlo assessment of the impact of oscillatory and pulsating boundary conditions on the flow through porous media. Transport in Porous Media. 123(1), 125--146 (2018)

J. Chen, D. Weihs, F.J. Vermolen. A model for cell migration in non-isotropic fibrin networks with an application to pancreatic tumor islets. Biomechanics and Modelling in Mechanobiology. 17(2), 367--386 (2018)

F.J. Vermolen, A. Segal. On an integration rule for products of barycentric coordinates over simplexes in Rn. Journal of Computational and Applied Mathematics. 330, 289--294 (2018)

J. Chen, D. Weihs, F.J. Vermolen. Monte Carlo uncertainty quantification in modelling cell deformation during cancer metastasis. Proceedings of the CMMBE 2018 conference (2018)

F.J. Vermolen, L.Y.D. Crapts, J.K. Ryan. A Discontinuous Galerkin Model for the Simulation of Chemotaxis Processes: Application to Stem Cell Injection After a Myocardial Infarction: Discontinuous Galerkin Methods. In: Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes. Chapter 6: 95--115 (2018)

F.J. Vermolen, S.D. Harrevelt, A. Gefen, D. Weihs. A Particle Finite Element–Based Framework for Differentiation Paths of Stem Cells to Myocytes and Adipocytes: Hybrid Cell–Based and Finite Element Modeling. In: Numerical Methods and Advanced Simulation in Biomechanics and Biological Processes. Chapter 9: 171--185 (2018)

F.J. Vermolen, D.C. Koppenol. Continuum scale models for the evolution of hypertrophic scars and contractions after burn injuries. In: Computer Methods in Biomechanics and Biomedical Engineering, Springer, Chan. 99--106 (2018)

M. Rahrah, F.J. Vermolen. Uncertainty Quantification in Injection and Soil Characteristics for Biot’s Poroelasticity Model. In: European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2017), 645--652, Springer (2018)

F.J. Vermolen. Uncertainty Assessment of a Hybrid Cell-Continuum Based Model for Wound Contraction. In: European Conference on Numerical Mathematics and Advanced Applications (ENUMATH 2017), 247--255, Springer (2018)

D.C. Koppenol, F.J. Vermolen. Biomedical implications from a morphoelastic continuum model for the simulation of contracture formation in skin grafts that cover excised burns. Biomechanics and modeling in mechanobiology, 16(4), 1187-1206 (2017)

D.C. Koppenol, F.J. Vermolen, G.V. Koppenol-Gonzalez, F.B. Niessen. A mathematical model for the simulation of the contraction of burns. Journal of mathematical biology, 75 (1), 1--31 (2017)

D.C. Koppenol, F.J. Vermolen, F.B. Niessen, P.P.M. van Zuijlen, C. Vuik. A biomechanical mathematical model for the collagen bundle distribution-dependent contraction and subsequent retraction of healing dermal wounds. Biomechanics and modeling in mechanobiology, 16(1), 345--361 (2017)

D.C. Koppenol, F.J. Vermolen, F.B. Niessen, P.P.M. van Zuijlen, C. Vuik. A mathematical model for the simulation of the formation and the subsequent regression of hypertrophic scar tissue after dermal wounding. Biomechanics and modeling in mechanobiology. 16(1), 15--32 (2017)

F.D. Bookholt, H.N. Monsuur, S. Gibbs, F.J. Vermolen. Mathematical modelling of angiogenesis using continuous cell-based models. Biomechanics and modeling in mechanobiology. 15 (6), 1577--1600 (2016)

D. Weihs, A. Gefen, F.J. Vermolen.Review on experiment-based two-and three-dimensional models for wound healing. Interface focus. 6 (5), 20160038 (2016)

L.A. Lopez Pena, B.J. Meulenbroek, FJ Vermolen. A Network Model for the Kinetics of Bioclogged Flow Diversion for Enhanced Oil Recovery. ECMOR XV-15th European Conference on the Mathematics of Oil Recovery, cp-494-00031 (2016)

N.V. Budko, B. van Duijn, S. Hille, F.J. Vermolen. Modeling Oxygen Consumption in Germinating Seeds. European Consortium for Mathematics in Industry, 193--200 (2016)

W.M. Boon, D.C. Koppenol, F.J. Vermolen. A multi-agent cell-based model for wound contraction. Journal of Biomechanics. 49 (8), 1388-1401 (2016)

F.J. Vermolen, E. Arkesteijn, A. Gefen. Modelling the immune system response to epithelial wound infections. Journal of Theoretical Biology 393, 158--169 (2016)

W.K. van Wijngaarden, L.A. van Paassen, F.J. Vermolen, G.A.M. van Meurs, C. Vuik. Simulation of front instabilities in density-driven flow, using a reactive transport model for Biogrout combined with a randomly distributed permeability field. Transport in Porous Media, 112 (2), 333-359 (2016)

W.K. van Wijngaarden, L.A. van Paassen, F.J. Vermolen, G.A.M. van Meurs, C. Vuik. A reactive transport model for biogrout compared to experimental data. Transport in Porous Media 111 (3), 627-648 (2016)

M. Dudaie, D. Weihs, F.J. Vermolen, A. Gefen. Modeling migration in cell colonies in two and three dimensional substrates with varying stiffnesses. In Silico Cell and Tissue Science 2 (1), 2 (2015)

F.J. Vermolen. Particle methods to solve modelling problems in wound healing and tumor growth. Computational Particle Mechanics. 2 (4), 381--399 (2015)

F.J. Vermolen, A. Gefen. Semi-stochastic cell-level computational modelling of cellular forces: application to contractures in burns and cyclic loading. Biomechanics and modeling in mechanobiology. 14 (6), 1181--1195 (2015)

F.J. Vermolen, R.P. Van der Meijden, M. Van Es, A. Gefen, D. Weihs. Towards a mathematical formalism for semi-stochastic cell-level computational modeling of tumor initiation. Annals of biomedical engineering. 43 (7), 1680--1694 (2015)

N.V. Budko, F.J. Vermolen. Phase-space analysis of large ODE systems using a low-dimensional conservation law. arXiv preprint. arXiv:1503.00922 (2015)

N.V. Budko, F.J. Vermolen. Phase-space approach to multi-population dynamics. arXiv preprint. arXiv:1503.00922 (2015)

L. Geris, F.J. Vermolen. In silico cell and tissue science. In Silico Cell and Tissue Science. 1 (1), 1 (2014)

F.J. Vermolen, M.M. Mul, A. Gefen. Semi-stochastic cell-level computational modeling of the immune system response to bacterial infections and the effects of antibiotics. Biomechanics and Modeling in Mechanobiology. 13 (4), 713--734 (2014)

P.A. Prokharau, F.J. Vermolen, J.M. García-Aznar. A mathematical model for cell differentiation, as an evolutionary and regulated process. Computer methods in biomechanics and biomedical engineering. 17 (10), 1051--1070 (2014)

W.K. van Wijngaarden, F.J. Vermolen, G.A.M. van Meurs, C. Vuik. A robust method to tackle pressure boundary conditions in porous media flow: application to biogrout. Computational Geosciences. 18 (2), 103-0115 (2014)

S.V. Zemskov, H.M. Jonkers, F.J. Vermolen. A mathematical model for bacterial self-healing of cracks in concrete. Journal of Intelligent Material Systems and Structures. 25 (1), 4--12 (2014)

D. Den Ouden, L. Zhao, C. Vuik, J. Sietsma, F.J. Vermolen. Modelling precipitate nucleation and growth with multiple precipitate species under isothermal conditions: Formulation and analysis. Computational materials science. 79, 933-943 (2014)

W.K. Van Wijngaarden, F.J. Vermolen, G.A.M. van Meurs, C. Vuik. A mathematical model for Biogrout. Computational Geosciences. 17 (3), 463--478 (2013)

D. Den Ouden, A. Segal, F.J. Vermolen, L. Zhao, C. Vuik, J. Sietsma. Application of the level-set method to a mixed-mode driven Stefan problem in 2 and 3 dimensions. Computing. 95 (1), 553--572 (2013)

F.J. Vermolen, A. Gefen. A phenomenological model for chemico-mechanically induced cell shape changes during migration and cell–cell contacts. Biomechanics and modeling in mechanobiology. 12 (2), 301-323 (2013)

S.V. Zemskov, B. Ahmad, O. Copuroglu, F.J. Vermolen. Modeling of a self-healing process in blast furnace slag cement exposed to accelerated carbonation. Journal of Physics: Conference Series. 410 (1), 012088 (2013)

F.J. Vermolen, A. Gefen. A semi-stochastic cell-based model for in vitro infected ‘wound’healing through motility reduction: a simulation study. Journal of theoretical biology. 318, 68-80 (2013)

D. den Ouden, F.J. Vermolen, L. Zhao, C. Vuik, J Sietsma. Application of the Level-Set Method to a Mixed-Mode and Curvature Driven Stefan Problem. In: Numerical Mathematics and Advanced Applications 2011, 141--148 (2013)

D. Ibrahim, F.J. Vermolen, C. Vuik. On the Density-Enthalpy Method for the 2D Darcy Flow. In: Numerical Mathematics and Advanced Applications 2011, 519--527 (2013)

F.J. Vermolen. On the Construction of Analytic Solutions to a Visco–Elasticity Model for Soft Tissues. In: Numerical Mathematics and Advanced Applications 2011, 607--615 (2013)

P.A. Prokharau, F.J. Vermolen. Stability analysis for a peri-implant osseointegration model. Journal of mathematical biology. 66 (1-2), 351--382 (2013)

P.A. Prokharau, F.J. Vermolen, J.M. García-Aznar. Numerical method for the bone regeneration model, defined within the evolving 2D axisymmetric physical domain. Computer Methods in Applied Mechanics and Engineering. 253, 117--145 (2013)

F.J. Vermolen, A. Gefen. Wound healing: multi-scale modeling. In: Multiscale Computer Modeling in Biomechanics and Biomedical Engineering, Springer, Berlin, 321-345 (2013)

W.K. Van Wijngaarden, F.J. Vermolen, G.A.M. Van Meurs, C. Vuik. Various flow equations to model the new soil improvement method Biogrout. In: Numerical Mathematics and Advanced Applications 2011, 633--641 (2013)

F.J. Vermolen, C. Vuik, A. Segal. Deflation in Preconditioned Conjugate Gradient Methods for finite element problems. In: Conjugate Gradient Algorithms and Finite Element Methods, 103 (2013)

F.J. Vermolen, E. Javierre. A finite-element model for healing of cutaneous wounds combining contraction, angiogenesis and closure. Journal of mathematical biology 65 (5), 967--996 (2012)

E. Javierre, S.J. García, J.M.C. Mol, F.J. Vermolen, C. Vuik, S. van der Zwaag. Tailoring the release of encapsulated corrosion inhibitors from damaged coatings: controlled release kinetics by overlapping diffusion fronts. Progress in Organic Coatings. 75 (1--2), 20--27 (2012)

P.A. Prokharau, F.J. Vermolen, J.M. García-Aznar. Model for direct bone apposition on pre-existing surfaces, during peri-implant osseointegration. Journal of theoretical biology. 304, 131--142 (2012)

W.K. van Wijngaarden, F.J. Vermolen, G.A.M. van Meurs, C. Vuik. A mathematical model and analytical solution for the fixation of bacteria in biogrout. Transport in porous media 92 (3), 847--866 (2012)

F.J. Vermolen, O. van Rijn. A Mathematical Model for Wound Contraction and Angiogenesis. In: Jamie Davis (ed)Tissue Regeneration-From Basic Biology to Clinical Application, InTech (2012)

F.J. Vermolen, A. Gefen, J.W.C. Dunlop. In vitro “wound” healing: Experimentally based phenomenological modeling. Advanced Engineering Materials 14 (3), B76-B88 (2012)

F.J. Vermolen, A. Gefen. A semi-stochastic cell-based formalism to model the dynamics of migration of cells in colonies. Biomechanics and modeling in mechanobiology. 11 (1--2), 183--195 (2012)

F.J. Vermolen, A. Segal, A. Gefen. A pilot study of a phenomenological model of adipogenesis in maturing adipocytes using Cahn–Hilliard theory. Medical & biological engineering & computing 49 (12), 1447--1457 (2012)

S. Mazumder, F.J. Vermolen, J. Bruining. Analysis of a model for anomalous-diffusion behavior of CO2 in the macromolecular-network structure of coal. SPE Journal 16 (04), 856--863 (2011)

S.V. Zemskov, H.M. Jonkers, F.J. Vermolen. Two analytical models for the probability characteristics of a crack hitting encapsulated particles: Application to self-healing materials. Computational materials science. 50 (12), 3323--3333 (2011)

S.V. Zemskov, H.M. Jonkers, F.J. Vermolen. Mathematical models to predict the critical conditions for bacterial self-healing of concrete. International Conference on Mathematical Modeling and Computational Physics, 108--121 (2011)

E. Javierre, S.J. García, J.M.C. Mol, F.J. Vermolen, C. Vuik, S. van der Zwaag. Model based tuning of the release of self healing agents from organic coatings: From Fickian to controlled release kinetics. ICSHM 2011: Proceedings of the 3rd International Conference on Self-Healing Materials (2011)

D. den Ouden, F.J. Vermolen, L. Zhao, C. Vuik, J. Sietsma. Modelling of particle nucleation and growth in binary alloys under elastic deformation: An application to a Cu–0.95 wt% Co alloy. Computational materials science. 50 (8), 2397--2410 (2011)

W.K. van Wijngaarden, F.J. Vermolen, G.A.M. van Meurs, C. Vuik. Modelling biogrout: a new ground improvement method based on microbial-induced carbonate precipitation. Transport in porous media 87 (2), 397--420 (2011)

P. Prokharau, F.J. Vermolen, J.M. Garcia-Aznar. Evolutionary cell differentiation approach in a peri-implant osseointegration model. Proceedings of II International Conference on Tissue Engineering, 149--156 (2011)

D. Ouden, F.J. Vermolen, L. Zhao, C. Vuik, J. Sietsma. Mathematical modelling of NbC particle nucleation and growth in an HSLA steel under elastic deformation. Solid State Phenomena. 172, 893--898 (2011)

D.X. Du, P.L.J. Zitha, F.J. Vermolen. Numerical analysis of foam motion in porous media using a new stochastic bubble population model. Transport in porous media 86 (2), 461--474 (2011)

S.V. Zemskov, H.M. Jonkers, F.J. Vermolen. An analytical model for the probability characteristics of a crack hitting an encapsulated self-healing agent in concrete. International Workshop on Computer Algebra in Scientific Computing, 280--292 (2011)

D. Ibrahim, F.J. Vermolen, C. Vuik. Application of the numerical density-enthalpy method to the multi-phase flow through a porous medium. Procedia Computer Science 1 (1), 781--790 (2010)

F.J. Vermolen, E. Javierre. Computer simulations from a finite-element model for wound contraction and closure. Journal of Tissue Viability 19 (2), 43--53 (2010)

S.V. Zemskov, F.J. Vermolen, E. Javierre, C. Vuik. A Cut-Cell Finite-Element Method for a Discontinuous Switch Model for Wound Closure. In: Numerical Mathematics and Advanced Applications 2009, 929--936 (2010)

WK Van Wijngaarden, FJ Vermolen, GAM Van Meurs, C Vuik. Modelling the new soil improvement method Biogrout: extension to 3D. Numerical Mathematics and Advanced Applications 2009, 893--900 (2010)

E. Javierre, F.J. Vermolen, C. Vuik, S. van der Zwaag. A mathematical analysis of physiological and morphological aspects of wound closure. Journal of mathematical biology. 59 (5), 605--630 (2009)

L. Zhao, F.J. Vermolen, J. Sietsma, S. van der Zwaag. Physical simulation of thermally induced martensite formation from retained austenite in TRIP steels. Journal of Materials Sciences and Technology 19 (4), 105--108 (2009)

F.J. Vermolen, E. Javierre. On the construction of analytic solutions for a diffusion–reaction equation with a discontinuous switch mechanism. Journal of computational and applied mathematics. 231 (2), 983--1003 (2009)

F.J. Vermolen. Simplified finite-element model for tissue regeneration with angiogenesis. Journal of engineering mechanics 135 (5), 450--460 (2009)

E. Javierre, F.J. Vermolen, C. Vuik, P. Wesseling, S. van der Zwaag. Computing Interfaces in Diverse Applications.

ECCOMAS Multidisciplinary Jubilee Symposium, 327-341 (2009)

F.J. Vermolen, M.G. Ghararoo, P.L.J. Zitha, J. Bruining. Numerical Solutions of Some Diffuse Interface Problems: The Cahn-Hilliard Equation and the Model of Thomas and Windle. International Journal for Multiscale Computational Engineering. 7 (6), 523--543 (2009)

F.J. Vermolen, A. Andreykiv, E.M. Van Aken, J.C. Van der Linden, E. Javierre, A. van Keulen. A suite of mathematical models for bone ingrowth, bone fracture healing and intra-osseous wound healing, Advanced Computational Methods in Science and Engineering, 289--314 (2009)

F.J. Vermolen, E. Javierre. A suite of continuum models for different aspects in wound healing. Bioengineering Research of Chronic Wounds, 127--168 (2009)

F.J. Vermolen, E.M. van Aken, J.C. van der Linden, A. Andreykiv. A finite element model for bone ingrowth into a prosthesis. In: Numerical Mathematics and Advanced Applications, 99--106 (2008)

E. Javierre, F.J. Vermolen, C. Vuik, S. van der Zwaag. Numerical modelling of epidermal wound healing. In: Numerical Mathematics and Advanced Applications, 83--90 (2008)

F.J. Vermolen, E. Javierre, C. Vuik, L. Zhao, S. van der Zwaag. A three-dimensional model for particle dissolution in binary alloys. Computational materials science 39 (4), 767--774 (2007)

E. Javierre, C. Vuik, F.J. Vermolen, A. Segal. A level set method for three dimensional vector Stefan problems: Dissolution of stoichiometric particles in multi-component alloys. Journal of Computational Physics 224 (1), 222--240 (2007)

F.J. Vermolen. On similarity solutions and interface reactions for a vector-valued Stefan problem. Nonlinear Analysis: Modelling and Control. 12, 269--288 (2007)

F.J. Vermolen, M.W.G. van Rossum, E. Javierre, J.A. Adam. Modeling of self healing of skin tissue. Self Healing Materials. 337--363 (2007)

F.J. Vermolen, E. van Baaren, J.A. Adam. A simplified model for growth factor induced healing of wounds. Mathematical and computer Modelling 44 (9--10), 887--898 (2006)

P.L.J. Zitha, D.X. Du, F.J. Vermolen. Numerical Analysis of Foam Motion in Porous Media Using a New Stochastic Bubble Population Model. ECMOR X-10th European Conference on the Mathematics of Oil Recovery, cp-23-00002 (2006)

F.J. Vermolen, P.L.J. Zitha. Deflation Accelerated Preconditioned Conjugate Gradient Method in Finite Element Methods in Oil Reservoirs. ECMOR X-10th European Conference on the Mathematics of Oil Recovery, cp-23-00054 (2006)

E. Javierre, C. Vuik, F.J. Vermolen, S. van der Zwaag. A comparison of numerical models for one-dimensional Stefan problems. Journal of Computational and Applied Mathematics. 192 (2), 445--459 (2006)

L. Zhao, F.J. Vermolen, J. Sietsma, A. Wauthier. Cementite dissolution at 860 C in an Fe-Cr-C steel. Metallurgical and Materials Transactions A 37 (6), 1841--1850 (2006)

P.L.J. Zitha, F.J. Vermolen. Self-similar solutions for the foam drainage equation. Transport in porous media. 63 (1), 195-200 (2006)

E. Javierre, C. Vuik, F.J. Vermolen, A. Segal, S. van der Zwaag. Higher dimensional numerical simulations of precipitate dissolution in multi-component aluminium alloys. ECCOMAS CFD 2006: Proceedings of the European Conference on Computational Mathematics (2006)

E. Javierre, C. Vuik, F.J. Vermolen, A. Segal, S. van der Zwaag. The level set method for solid-solid phase transformations. In: Numerical Mathematics and Advanced Applications. 712--719 (2006)

F.J. Vermolen, C. Vuik. Solution of vector Stefan problems with cross-diffusion. Journal of Computational and Applied mathematics. 176 (1), 179--201 (2005)

N.C.W. Kuijpers, F.J. Vermolen, C. Vuik, P.T.G. Koenis, K.E. Nilsen, S. van der Zwaag. The dependence of the β-AlFeSi to α-Al (FeMn) Si transformation kinetics in Al–Mg–Si alloys on the alloying elements. Materials Science and Engineering: A 394 (1--2), 9--19 (2005)

F.J. Vermolen, C. Vuik, S. van der Zwaag. Cross-diffusion controlled particle dissolution in metallic alloys. Computing and visualization in science. 8 (1), 27--33 (2005)

F.J. Vermolen, C. Vuik, E. Javierre, S. van der Zwaag. Review on some Stefan problems for particle dissolution in solid metallic alloys. Nonlinear analysis: modelling and control 10 (3), 257--292 (2005)

F.J. Vermolen, C. Vuik, S. van der Zwaag. Advanced Models for Particle Dissolution in Multi‐Component Alloys. In: Solid State Transformation and Heat Treatment, 53--60 (2004)

F.J. Vermolen, C. Vuik, A. Segal. Deflation accelerated parallel preconditioned Conjugate Gradient method in Finite Element problems. In: Numerical Mathematics and advanced applications, 825--833 (2004)

N.C.W. Kuijpers, F.J. Vermolen, C. Vuik, S. van der Zwaag. Predicting the Effect of Alloy Composition on the Intermetallic Phase Transformation Kinetics in 6 XXX Extrusion Alloys. Materials Forum 28, 1040--1045 (2004)

F.J. Vermolen, C. Vuik, A. Segal. Deflation in preconditioned conjugate gradient methods for finite element problems.

Conjugate Gradient Algorithms and Finite Element Methods. 103--129 (2004)

N.C.W. Kuijpers, F.J. Vermolen, C. Vuik, S. van der Zwaag. A Model of the β-AlFeSi to α-Al(FeMn)Si Transformation in Al-Mg-Si Alloys. Materials transactions 44 (7), 1448--1456 (2003)

P.L.J. Zitha, C.W. Botermans, J. Hoek, F.J. Vermolen. Control of flow through porous media using polymer gels. Journal of applied physics. 92 (2), 1143--1153 (2002)

L. Boukhelifa, P.L.J. Zitha, F.J. Vermolen. Numerical analysis of layer and bridging adsorption of flexible polymers in porous media. Colloids and Surfaces A: Physicochemical and Engineering Aspects. 24 (1--3), 153--168 (2002)

F.J. Vermolen, C. Vuik, S. van der Zwaag. A mathematical model for the dissolution of stoichiometric particles in multi-component alloys. Materials Science and Engineering. A328 (1-2), 14--25 (2002)

F.J. Vermolen, P.L.J. Zitha, J. Bruining. A model for a viscous preflush prior to gelation in a porous medium. Computing and visualization in science. 4 (3), 205--212 (2002)

C. Vuik, J. Frank. F.J. Vermolen. Parallel Deflated Krylov methods for incompressible flow. In: Parallel Computational Fluid Dynamics, 381--388 (2002)

F.J. Vermolen, J. Bruining, C.J. van Duijn. Gel placement in porous media: constant injection rate. Transport in porous media. 44 (2), 247--266 (2001)

F.J. Vermolen, C. Vuik. A mathematical model for the dissolution of particles in multi-component alloys. Journal of computational and applied mathematics. 126 (1--2), 233--254 (2000)

C. Vuik, A. Segal, F.J. Vermolen. A conserving discretization for a Stefan problem with an interface reaction at the free boundary. Computing and visualization in science. 3 (1-2), 1090-114 (2000)

S.P. Chen, M.S. Vossenberg, F.J. Vermolen, J. van de Langkruis, S. van der Zwaag. Dissolution of β particles in an AlMgSi alloy during DSC runs. Materials Science and Engineering. A 272 (2), 250--256 (1999)

S.P. Chen, M.S. Vossenberg, F.J. Vermolen, J. van de Langkruis, S. van der Zwaag.Dissolution of beta particles in an AlSiMg alloy. Materials Science and Engineering-A-Structural Materials 272 (2), 250--256 (1999)

F.J. Vermolen, C. Vuik. A vector-valued Stefan problem from aluminium industry. Nieuw archief voor wiskunde. 17, 205--218 (1999)

P.L.J. Zitha, F.J. Vermolen, J. Bruining. Modification of two phase flow properties by adsorbed polymers and gels. SPE European Formation Damage Conference. 26 (1999)

F.J. Vermolen, C. Vuik, S. van der Zwaag. A mathematical model for the dissolution kinetics of Mg2Si-phases in Al–Mg–Si alloys during homogenisation under industrial conditions. Materials Science and Engineering. A 254 (1--2), 13--32 (1998)

F.J. Vermolen, C. Vuik. A numerical method to compute the dissolution of second phases in ternary alloys. Journal of computational and applied mathematics. 93 (2), 123--143 37 (1998)

F.J. Vermolen, C. Vuik, S. van der Zwaag. The dissolution of a stoichiometric second phase in ternary alloys: a numerical analysis. Materials Science and Engineering. A 246 (1--2), 93--103 (1998)

A. Segal C. Vuik, F.J. Vermolen. A conserving discretization for the free boundary in a two-dimensional Stefan problem. Journal of Computational Physics. 141 (1), 1--21 (1998)

F.J. Vermolen, C. Vuik, S. van der Zwaag. Modelling The Microstructural Changes During The Homogenisation of Extrudable Aluminium Alloys. Journal of the Mechanical Behavior of Materials 9 (2), 115--120 (1998)

F.J. Vermolen, C. Vuik, S. van der Zwaag. A numerical analysis for the dissolution of second phase particles in ternary alloys. WIT Transactions on Modelling and Simulation. 17 ISSN 1743-355X (1997)

F.J. Vermolen, H.M. Slabbekoorn, S. van der Zwaag. The apparent activation energy for the dissolution of spherical Si-particles in AlSi-alloys. Materials Science and Engineering. A 231 (1--2), 80--89 (1997)

F.J. Vermolen, P. van Mourik, S. van der Zwaag. Analytical approach to particle dissolution in a finite medium. Materials science and technology. 13 (4), 308--312 (1997)

F.J. Vermolen, S. van der Zwaag. A numerical model for the dissolution of spherical particles in binary alloys under mixed mode control. Materials Science and Engineering. A 220 (1--2), 140--146 (1996)

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