Ruili Zhang
PhD student
Ir. at NWPU in 2010

Main project: Adaptive curvilinear meshing
Funding: ERC
The generation of adaptive meshes has been one thriving research area in the last two decades.The generation of adaptive anisotropic meshes allows to dramatically reduce the number of degrees of freedom required to obtain a given accuracy.

There is a growing consensus in the computational mechanics community that state of the art solver technology requires, and will continue to require too extensive computational resources to provide the necessary resolution for a broad range of demanding applications, even at the rate that computational power increases. The requirement for high resolution naturally leads us to consider methods which have a higher order of grid convergence than the classical (formal) 2nd order provided by most industrial grade codes. This indicates that higher-order discretization methods will replace at some point the current finite volume and finite element solvers, at least for part of their applications.

The development of high-order numerical technologies for engineering analysis has been underway for many years now. For example, Discontinuous Galerkin methods (DGM) have been largely studied in the literature, initially in a theoretical context, and now from the application point of view.

In many contributions, it is shown that the accuracy of the method strongly depends on the accuracy of the geometrical discretization. Consequently, it is necessary to address the problem of generating the high- order meshes that are needed to fully benefit from high-order methods. Our team at UCL was one of the pioneers in curvilinear meshing. This research project aims at developing a new area of research, namely curvilinear mesh adaptation. The underlying research question can be stated as follow: let f(x,y) be a smooth function defined on the unit square. What is the mesh that minimizes the approximation error || f - Pf || where || . || is the L2 norm and P the Clément interpolant. Two main questions will have to be addressed: (i) how can we define a suitable metric that actually represents the approximation error and (ii) how do we build a mesh that is somehow aligned with the geodesics of the metric.

IMMC main research direction(s):
Computational science

Research group(s): MEMA