Adaptive gradient-augmented level set method with multiresolution error estimation

A space–time adaptive scheme is presented for solving advection equations in two space dimensions. The gradient-augmented level set method using a semi-Lagrangian formulation with backward time integration is coupled with a point value multiresolution analysis using Hermite interpolation. Thus locally refined dyadic spatial grids are introduced which are efficiently implemented with dynamic quadtree data structures. For adaptive time integration, an embedded Runge–Kutta method is employed. The precision of the new fully adaptive method is analysed and speed up of CPU time and memory compression with respect to the uniform grid discretization are reported.

Dmitry Kolomenskiy, Jean-Christophe Nave, Kai Schneider. Adaptive gradient-augmented level set method with multiresolution error estimation. Journal of Scientific Computing, Springer Verlag, 2016, 66 (1), pp.116-140. ⟨10.1007/s10915-015-0014-7⟩. ⟨hal-01146954⟩

Journal: Journal of Scientific Computing

Date de publication: 01-01-2016

Auteurs:
  • Dmitry Kolomenskiy
  • Jean-Christophe Nave
  • Kai Schneider

Digital object identifier (doi): http://dx.doi.org/10.1007/s10915-015-0014-7

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