Jean-François Remacle
Recent publications

After his Engineering Degree at the University of Liège in Belgium in 1992, Jean-François Remacle obtained in 1997 a Ph.D. from the same University. He then spent two years at the Ecole Polytechnique de Montréal as a post-doctoral fellow of Prof. F. Trochu, followed by three years at Rensselaer Polytechnic Institute in the research team of Prof. M. Shephard (one year as research associate followed by two years as research assistant professor).

It was during his stay at Rensselaer that Pr. Remacle started to work closely with Mark Shephard on mesh generation. Pr. Shephard's seminal work on mesh generation is one of the most important contributions ever. It was also during that stay that Pr. Remacle started the development of Gmsh, the open source mesh generator.

After these five years in Northern America, Jean-François Remacle joined the Université catholique de Louvain in 2002 as an assistant Professor. He then became Associate Professor in 2005 and Full Professor in 2012. In the following years of his return to Europe, Pr. Remacle dedicated a large part of his research to mesh generation.

IMMC main research direction(s):
Computational science

finite elements
mesh generation

Research group(s): MEMA

PhD and Post-doc researchers under my supervision:

Automatic hexahedral mesh generation for boundary layers
Christos Georgiadis

The main objective of our work is to provide with a fast and reliable method for generating boundary layer meshes. We follow a strategy that uses direction fields and a frontal point insertion strategy. The input of our algorithm is an initial triangular mesh of our domain and a direction field calculated on it. The goal is to compute the vertices of the final mesh by an advancing front strategy along the direction field. The final mesh will consists of right angle triangles, optimal for merging into quadrilaterals.

Pierre-Alexandre Beaufort

The aim of the 'ARC WAVES project 15/19-03' was to perform seismic migration from nonstandard geometries, i.e. geometries that are not defined properly; typically, computer aided-design (CAD) is not available.
My thesis was one part of this project: enabling mesh generation on those nonstandard geometries.
The challenge is to deal with a class of geometries which is a nightmare for numerical computations.
Information has to be recovered in order to produce high quality mesh, such as full quadrangles (2D) and dominant hexahedra (3D).
Surface parameterization enables mesh generation, while crossfields and 3D frames guide quadrangulations and hexahedrizations (respectively).

Further details on

Multithreaded Mesh Generation
Célestin Marot

The main goal of this thesis is to speedup tetrahedral mesh generation by an order of magnitude. To do so, we are parallelizing and enhancing the whole mesh generation process. Promising results are uncovered at

Curvilinear mesh adaptation
Amaury Johnen

graduated as a physician engineer at the University of Liège (Belgium) in 2011. Then he accomplished a PhD in the topic of quadrangular mesh generation and cuvilinear mesh validation, under the supervision of professor Christophe Geuzaine. He started a postdoctoral research in January 2016 under the supervision of professor Jean-François Remacle for working on curvilinear mesh generation, hex-dominant mesh generation and mesh validation.

All-hexahedral meshing
Kilian Verhetsel

While there exist algorithms to generate hex-dominant meshes, which contain a majority of hexahedra as well as a mixture of tetrahedra, prisms, and pyramids, automatically generating hexahedral meshes with elements of a reasonable quality is not currently possible. Subdividing the elements of a hex-dominant mesh could allow hexahedral meshes to be generated automatically, but the best known subdivision of a pyramid requires too many elements to be practical (see figure).

My work focuses on finding all-hexahedral meshes of small models such as this pyramid by first finding a topological solution using combinatorial search techniques. A geometric mesh will then be produced by finding coordinates for each vertex in the mesh.

François Henrotte

completed his Engineering Degree in 1991 and his PhD in 2000, both at the University of Liège in Belgium. He then spent 4 years at the Katholieke Universiteit Leuven and 6 years at the Institut für Elektrische Maschinen in Aachen, Germany, and is now with the UCL and the ULiège. Developer in the open-source packages Gmsh, GetDP and Onelab, he has also developed skills in the multiphysics simulation of electrical machines and drives. His main interests are finite element analysis, numerical modeling, electromechanical coupling, material properties (hysteresis, iron losses, superconductors), applied mathematics (differential geometry, algebraic topology, convex analysis, dual analysis, energy methods), multiscale methods, sensitivity and optimization.

Poly-cube decomposition of 3D volumes
Jovana Jezdimirovic

The aim of the research thesis is to push forward the state-of-the-art of mesh generation and propose for the first time a methodology that allows to automatically create structured multi-block meshes for general 3D domains. For that, an innovative approach that enables automatic decomposition of a general 3D domain into “poly-cubes” is proposed. A “poly-cube” map is a mechanism that allows a seamless parameterization of a 3D domain. The “poly-cube” decomposition provides the multi-block structure that is needed for structured meshing. In order to achieve this goal, the first part of the thesis is dedicated to the development of a “poly-quad” decomposition of a general 2D surface. It is relied on solving adequate Ginzburg Landau equations in order to develop a robust procedure that generates cross fields and locates critical points. Existence and location of critical points – represented as elliptic Fekete points are proved in recent results by Jezdimirovic, 2017. Further, critical points will be connected through the integral lines leading to an automatic decomposition of the domain into “quadrilaterals”. In the next step, the presented idea will be extended to 3D in order to create automatic algorithm for the “poly-cube” decomposition of 3D volumes.

Fast Helmholtz Solvers on Multi-Threaded Architectures
Ruiyang Dai

The Helmholtz equation arises in the study of various physical problems involving the propagation of waves, like electromagnetic radiation, seismology or acoustics. The goal of the project is to develop a Helmholtz solver that can accelerate high- frequency computations by at least one order of magnitude with respect to state-of-the art approaches. We propose to combine the following three ingredients to achieve a breakthrough in the solution of high-frequency Helmholtz problems:

1. Use a spectral finite element discretization on fully hexahedral meshes, both cartesian and non structured, for which AILU-type preconditioners can be efficiently applied on each subdomain of the geometry.

2. Develop a quasi-optimal DDM with a parallel sweeping-type preconditioner to allow for optimal convergence between the subdomains.

3. Implement the solver using a common kernel language to make the solver run on different devices (both GPU and CPU) using different thread programming interfaces (CUDA, OpenCL, and OpenMP).

3D crossfield generation for multibloc decomposition
Alexandre Chemin

The aim of the project is to realize multibloc decomposition of 3D volumes in order to generate full hex meshes. Nowadays, this kind of decomposition is done by hand. The purpose of this work is to be able to do it in an automatic way. In order to reach this objective, we are generating 3D crossfields in this volume to locate singular points and automatize the decomposition.

Automatic quadrilateral and hexahedral meshing
Maxence Reberol

My research interests are automatic block decomposition, quadrilateral meshing, hexahedral meshing and robust hex-dominant meshing.

Ginzburg-Landau and cross fields
Alexis Macq

Minimizers of so-called Ginzburg-Landau functionals are functions that minimize both their variations and the passage of their norms to values ​​different from 1. The arbitration between the importance of these two elements is done via a parameter epsilon. When epsilon is set to 0, the norm of the minimizers is 1 unless, if necessary, in a finite number of points. The presence of those points (called singular points) depends on the surface considered. The study of Ginzburg-Landau functionals is fashionable. In the context of mesh applications, these functionals are notably used for the construction of the most regular possible cross fields intended to be supports for the construction of quadrangular meshes as regular as possible. In this context, the singular points of minimizers of Ginzburg-Landau functionals can be mapped to singular nodes in the meshes we are trying to construct. Indeed, these meshes pursue the same two objectives as those involved in the Ginzburg-Landau functionals, namely, be as regular as possible and placing singular nodes in an optimized manner if singular nodes are necessary. In the case of non-constant curvature surfaces, the introduction of a covariant gradient can potentially make it possible to construct Ginzburg-Laudau functionals that are more suitable for these surfaces.
-Study of a Ginzburg-Landau fonctional containing a co-variant -gradient.
-Implementation of mathematical curvature for numerical applications.
-Mathematical study of cross fields.

Curvilinear mesh adaptation
Arthur Bawin

A pre-exascale Vortex Particle-mesh solver for complex Fluid-Structure Interaction problems.
Pierre Balty

We present an accurate and highly scalable vortex particle method builds upon a Multi-Resolution discretization (MR), an Immersed Interface Method (IIM) and efficient elliptic solvers to simulate bio-inspired locomotion in 3D. This project is intended to bring all the mentioned approaches together to the next scale of computational intensity and concurrency. The consistency between our Lagrangian formulation, these advanced numerical frameworks and a HPC-oriented implementation should unlock the full potential of Belgium’s next generation HPC architectures and thus, enable a leap in the scale of computable problems.

Three-dimensional multi-block decomposition for automatic hexahedral mesh generation and application to fluid flow simulations.
Mattéo Couplet

In computational physics, the vast majority of Partial Differential Equation (PDE) solvers rely on a spatial discretization of the bulk of the domain, typically a mesh. Thus far, geometrically complex domains are discretized predominantly using unstructured meshes, on which the PDE is subsequently solved using the Finite Element Method. Methods based on unstructured meshes are however inherently penalized in their computational efficiency. On the contrary, the regularity of block structured meshes can be leveraged to build efficient algorithms. For this reason, automatic generation of block-structured meshes is the holy grail of mesh generation.

A first objective of the research project is therefore to explore new approaches for generating multiblock decompositions of general 3D domains. We will build on the recent developments in 3D frame fields and aim at improving formulations based on the constrained minimization of an energy function. A second lead that will be explored is based on the decomposition of the domain in convex sub-regions, on which existing methods are more robust.

Constructing a new class of meshes is only relevant if those meshes are endowed with a true benefit in terms of CPU/GPU time and accuracy. A second objective is therefore to extend existing Computational Fluid
Dynamics technologies for Cartesian grids to multiblock grids. In particular, we want to take advantage of the conformal map-like nature of the mesh to increase computational performance, and also show how our methodology can be applied to models with moving or deforming boundaries.

Recent publications

See complete list of publications

Journal Articles

1. Verhetsel, Kilian; Pellerin, Jeanne; Remacle, Jean-François. Finding hexahedrizations for small quadrangulations of the sphere. In: ACM Transactions on Graphics, Vol. 38, no.4, p. 53(1-13) (2019). doi:10.1145/3306346.3323017.

2. Zhang, R.; Johnen, A.; Remacle, Jean-François. Curvilinear mesh adaptation. In: 27th International Meshing Roundtable, IMR 2018, Vol. 127, p. 57-69 (2019). doi:10.1007/978-3-030-13992-6_4.

3. Deschuyteneer, Aurélie; Zastavni, Denis; Remacle, Jean-François. A geometrical approach to assess levels of structural robustness in statically indeterminate concrete elements. In: Proceedings of IASS Annual Symposia, Vol. 2019, no. 12, p. 1-8 (2019).

4. Verhetsel, K.; Pellerin, J.; Remacle, Jean-François. A 44-element mesh of schneiders’ pyramid. In: 27th International Meshing Roundtable, IMR 2018, Vol. 127, p. 73-87 (2019). doi:10.1007/978-3-030-13992-6_5.

5. Remacle, Jean-François; Lambrechts, Jonathan. Fast and robust mesh generation on the sphere—Application to coastal domains. In: CAD Computer Aided Design, Vol. 103, p. 14-23 (2018). doi:10.1016/j.cad.2018.03.002.

6. Pellerin, Jeanne; Verhetsel, Kilian; Remacle, Jean-François. There are 174 subdivisions of the hexahedron into tetrahedra. In: ACM Transactions on Graphics, Vol. 37, no. 6 (2018) (2018). doi:10.1145/3272127.3275037.

7. Delandmeter, Philippe; Lambrechts, Jonathan; Legat, Vincent; Vallaeys, Valentin; Naithani, Jaya; Thiery, Wim; Remacle, Jean-François; Deleersnijder, Eric. A fully consistent and conservative vertically adaptive coordinate system for SLIM 3D v0.4 with an application to the thermocline oscillations of Lake Tanganyika. In: Geoscientific Model Development, Vol. 11, no.3, p. 1161-1179 (2018). doi:10.5194/gmd-11-1161-2018.

8. Remacle, Jean-François; Lambrechts, Jonathan. Fast and Robust Mesh Generation on the Sphere – Application to Coastal Domains. In: Procedia Engineering, Vol. 163, no. 1, p. 20-32 (2016). doi:10.1016/j.proeng.2016.11.011.

9. Toulorge, Thomas; Lambrechts, Jonathan; Remacle, Jean-François. Optimizing the geometrical accuracy of curvilinear meshes. In: Journal of Computational Physics, Vol. 310, no.1, p. 361-380 (2016). doi:10.1016/

10. Johnen, Amaury; Geuzaine, Christophe; Toulorge, Thomas; Remacle, Jean-François. Efficient Computation of the Minimum of Shape Quality Measures on Curvilinear Finite Elements. In: Procedia Engineering, Vol. 163, p. 328–339 (novembre 2016). doi:10.1016/j.proeng.2016.11.067.

Conference Papers

1. Verhetsel, Kilian; Pellerin, Jeanne; Remacle, Jean-François. A 44-element mesh of Schneiders' pyramid: Bounding the difficulty of hex-meshing problems.

2. Delandmeter, Philippe; Lambrechts, Jonathan; Vallaeys, Valentin; Naithani, Jaya; Remacle, Jean-François; Legat, Vincent; Deleersnijder, Eric. Modelling the oscillations of the thermocline in a lake by means of a fully consistent and conservative 3D finite-element model with a vertically adaptive mesh.

3. Verhetsel, Kilian; Pellerin, Jeanne; Johnen, Amaury; Remacle, Jean-François. Solving the Maximum Weight Independent Set Problem: Application to Indirect Hexahedral Mesh Generation.

4. Delandmeter, Philippe; Chen, Wei; Deleersnijder, Eric; Lambrechts, Jonathan; Legat, Vincent; Remacle, Jean-François; Wolanski, Eric; Marmorino, Geroge. Comparison of a satellite-derived high-resolution current map and numerical modelling of submesoscale eddies in a shallow-water domain.

5. Delandmeter, Philippe; Chen, Wei; Deleersnijder, Eric; Lambrechts, Jonathan; Legat, Vincent; Remacle, Jean-François; Marmorino, George; Wolanski, Eric. Comparison of a satellite-derived high-resolution current map and numerical modelling of submesoscale eddies in a shallow-water domain.

6. Delandmeter, Philippe; Lambrechts, Jonathan; Remacle, Jean-François; Legat, Vincent; Deleersnijder, Eric. An adaptive vertical coordinate system for a coastal flows discontinuous Galerkin finite element model.

7. Delandmeter, Philippe; Lambrechts, Jonathan; Remacle, Jean-François; Legat, Vincent; Wolanski, Eric; Deleersnijder, Eric. Influence of the vertical discretisation of SLIM 3D on a river plume modelling.

8. Lambrechts, Jonathan; Remacle, Jean-François; Dubois, Frédéric. Finite Element Model Of Grains/Fluid Flows.

9. Lambrechts, Jonathan; Seny, Bruno; Remacle, Jean-François. An efficient parallel implementation of explicit multirate Runge–Kutta schemes for discontinuous Galerkin computations.

10. Remacle, Jean-François; Lambrechts, Jonathan; Toulorge, Thomas; Johnen, Amaury; Geuzaine, Christophe. Optimizing the geometrical accuracy of 2D Finite Element curvilinear meshes.

Book Chapters

1. Chemin, Alexandre; Henrotte, François; Remacle, Jean-François; Van Schaftingen, Jean. Representing Three-Dimensional Cross Fields Using Fourth Order Tensors. In: 27th International Meshing Roundtable , Springer, Cham: Switzerland AG, 2019. 978-3-030-13991-9; 9783030139926. doi:10.1007/978-3-030-13992-6_6.

2. Geuzaine, Christophe; Johnen, Amaury; Lambrechts, Jonathan; Remacle, Jean-François; Toulorge, Thomas. The Generation of Valid Curvilinear Meshes. In: IDIHOM: Industrialization of High-Order Methods - A Top-Down Approach (Notes on Numerical Fluid Mechanics and Multidisciplinary Design; xxx), Springer International Publishing, 2015. 978-3-319-12885-6. doi:10.1007/978-3-319-12886-3_2.

3. Remacle, Jean-François; Toulorge, Thomas; Lambrechts, Jonathan. Robust untangling of curvilinear meshes. In: Proceedings of the 21st International Meshing Roundtable , Springer Berlin Heidelberg, 2013, p. 71-83. 978-3-642-33572-3. doi:10.1007/978-3-642-33573-0.

4. Marchandise, Emilie; Crosetto, Paolo; Geuzaine, Christophe; Remacle, Jean-François; Sauvage, Emilie. Quality open source mesh generation for cardiovascular flow simulations. In: Modeling of Physiological Flows (MS&A – Modeling, Simulation & Applications; xxx), Springer Italia Srl, 2012, 414 p.. 978-88-470-1934-8. doi:10.1007/978-88-470-1935-5_13.

5. Carrier-Baudouin, Tristan; Remacle, Jean-François; Marchandise, Emilie; Lambrechts, Jonathan. Lp lloyd's energy minimization for quadrilateral surface mesh generation. In: Proceedings of the 20th International Meshing Roundtable, IMR 2011 , xxx, 2011. 978-3-6422-4733-0.


1. Staten, Matthew; Persson, Per-Olof; Chrisochoides, Nikos; Ledoux, Franck; Martineau, David; Lewis, Katherine; Canann, Scott; Remacle, Jean-François; Wu, Xiaohua; Loeppky, Kathy. 23rd International Meshing Roundtable—Mesh modeling for simulations and visualization. Pergamon: Kidlington, 2016. 0010-4485.pages.

2. Hillewaert, Koen; Remacle, Jean-François; Chevaugeon, Nicolas; Bernard, Paul-Emile; Geuzaine, Philippe. Analysis of a hybrid p-Multigrid method for the discontinuous Galerkin discretisation of the Euler equations. P. Wesseling, E. Onate, J. Périaux (Eds): TU Delft, The Netherlands, 2006. 90-9020970-0.pages.

3. Hillewaert, Koen; Remacle, Jean-François; Chevaugeon, Nicolas; Bernard, Paul-Emile; Geuzaine, Philippe. Analysis of a Hybrid p-Multigrid Method for the Discontinuous Galerkin Discretization of the Euler Equations. P. Wesseling, E. Onate, J. Périaux (Eds): Egmond aan Zee, The Netherlands, 2006. 90-9020970-0.pages.