Second edition of the Mmg day

The Mmg platform is an open source platform gathering software dedicated to simplicial remeshing (2D, 3D surface, 3D volume).
It allows:

• to improve the mesh quality;
• to improve the boundary approximation of the domain;
• to adapt a mesh to an isotropic or anisotropic size map;
• to discretize a given isovalue of a function.

In this presentation, we will first focus on the 3D surface module of the platform and the boundary approximation. In a second part, we will detail the last release improvement.
Slides of the presentation

In this presentation, I introduce a Matlab package called MolSurfComp, which is newly-developed to compute molecular surfaces based on a Voronoi-type diagram. The highlight of this package is that all singularities are computed a priori and all possible inner holes can be detected. This package allows us to mesh different molecular surfaces and to compute the exact molecular volumes & areas.

On the fly parallel mesh adaptation capabilities of the YALES2 low-Mach number LES solver provide new attractive perspectives for unsteady simulations of SAFRAN combustion chambers. Different applications will be discussed during this presentation including fuel atomisation in injection systems, flame front tracking for combustor ignition and automatic mesh convergence. Numerical difficulties and perspectives will be discussed especially for massively parallel computations.

In our presentation we will introduce all the features, as well as the issues, found in the implementation of the MMG API in Kratos. In order to be able to present our implementation, we will first make an introduction to the capabilities and structure of the Kratos framework API. We will also highlight the documentation that is available to everyone so we can start using MMG in Kratos, as well as examples available in the platform to test the same.
We want to distinguish the different capabilities of our implementation:

• Remeshing according to the level-set: By using the gradient of a scalar variable we can compute an anisotropic metric, so we can produce an anisotropic remeshing. Example 1. Example 2. Example 3
• Remeshing according to the Hessian: Using the Hessian of a scalar variable we build a metric which we use to remesh. In order to consider vector variables, we do an intersection of each metric for every component. Example 1. Example 2. Example 3
• Metric Intersection Techniques: To be able to consider more than one metric measure we have implemented different techniques to be able to consider the intersection of different metrics.
• Remeshing with transfer of internal variables: We have implemented a formulation to transfer internal variables values for non-linear / historical problems, by using different techniques like CPT (Closest Point Transfer), LST (Least-square projection transfer) or SFT (Shape function transfer).
• Remeshing for numerical contact: It’s in development. We are using a modified version of Zienkievich and Zu’s superconvergent patch to remesh a numerical contact problem.

To finish our presentation, we will make a small introduction of the technical problems found during the implementation. Problems related with convection, updated API, or some bugs found..

Shape morphing or matching arises in a wide variety of situations in areas from biomedical engineering to computer graphics and scientific computing.
Beyond the specific stakes to each particular application, the general issue is to find one transformation from a given `template’ shape into a `target’ shape.
Such a transformation may be used as a means to appraise how much two shapes differ from one another or to achieve physically the transformation from the template to the target shape.
In this talk we address the following problem: given a “template” shape, numerically described by means of a computational mesh, and a “target” shape, known only via a signed distance function to its boundary, we aim at deforming iteratively the mesh of the template shape into a computational mesh of the target shape. To achieve this goal, we rely on techniques from shape optimization. Under the sole assumption that both shapes share the same topology, the desired transformation is realized as a sequence of elastic displacements, which are obtained by minimizing an energy functional based on the distance between the two shapes.
In doing so, it is expected that the deformation will be easier to achieve in numerical practice, and in particular by limiting the troubles due to mesh tangling.