Wavelet Particle Methods

We combine the adaptivity of Lagrangian particle methods with the multiresolution capabilities of wavelets. The goal is the achievement of high accuracy while minimizing the amount of computational elements. We rely on the remeshing of the particle methods in order to introduce multiresolution capabilities in a systematic framework. We utilize grids of variable resolutions as dictated by the wavelet analysis of the fields carried by the particles. The key computational challenge for this formulation is the processing and the communication patterns between the computational elements.

Solution (isosurface) of 3D passive advection of a scalar field using MRAG, every block has the same number of points, which in this case is  14x14x14. Here we used 4th order Interpolating Wavelets.


Multi-Resolution Adaptive Grids (MRAG)
We are developing a framework, MRAG, for particle methods that rely on adaptive grids in order to maintain their regularity and to introduce multiresolution capabilities.  The goal of MRAG is to provide an intuitive and powerful set of tools for an extensive usage of adapted grids. The MRAG-user  delegates the multi-resolution machinery to MRAG and concentrates his efforts in the simulation itself.
Objectives of this effort include: 
  • the exploitation of  the current hardware technology: MRAG should be able to run in parallel in a cluster, exploit the multi threading technology (multi cores) and take advantage of the massively multithreading technology (GPUs). 
  • provide mappings between multi-resolution grids and multi-resolution particles.
  • support time refinement (TR), i.e. exploit the fact that small scales in space can have small scale in time (multi-level time integration). 
MRAG, Multicores and GPUs
Currently MRAG is able to run generic 2D/3D grid-based simulations exploiting the multi-threading technology, GPU technology and is supporting TR. To validate the features supported by MRAG, we wrote 2D/3D client codes that simulate a passive scalar advection using an analytical velocity field, levelset reinitialization, diffusion and normal growth of a levelsets. 

Two dimensional advection of a level set starting from a circle. Approximation using an upwind scheme (left) and a WENO 3rd order scheme (right). 

The current implementaion of  MRAG enable ssimulations of advection of passive scalars and levelsets, levelset reinitializations, diffusion and comppressible flows with complex boundaries.

People: Diego RossinelliMichael BergdorfBabak Hejazialhosseini 

Funding: CO-ME, ETH Zurich