The RAMSES code, developed under the responsibility of R. Teyssier, is a development platform for solving mainly hyperbolic equation systems in an adaptive mesh refinement structure (AMR). For the time being, the basic mesh is Cartesian. We have planned to extend it to cylindrical and spherical meshing in 2004. The modules that have been developed so far are being massively used in cosmology (p...

Stochastic models of chemical systems are often analysed by solving the corresponding Fokker-Planck equation which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulati...

An experimental investigation on shape retrieval using Quadratic Polynomial Interpolation of Adjacent Landmarks (QPIAL), a newly proposed shape refinement method [1], is carried. Shape representation is a fundamental issue in the process of shape retrieval, a category of Content-Based Image Retrieval (CBIR). Many shape representations and shape refinement methods have been proposed. Fourier Des...

In this paper we propose an adaptive multilevel correction scheme to solve optimal control problems discretized with finite element method. Different from the classical adaptive finite element method (AFEM for short) applied to optimal control which requires the solution of the optimization problem on new finite element space after each mesh refinement, with our approach we only need to solve t...

We propose a new moving mesh method suitable for solving timedependent partial differential equations (PDEs) in R which have fine scale solution structures that develop or dissipate. A key feature of the method is its ability to add or remove mesh nodes in a smooth manner and that it is consistent with r-refinement schemes. Central to our approach is an implicit representation of a Lagrangian m...

We present a novel adaptive-resolution particle method for continuous parabolic problems. In this method, particles self-organize in order to adapt to local resolution requirements. This is achieved by pseudo forces that are designed so as to guarantee that the solution is always well sampled and that no holes or clusters develop in the particle distribution. The particle sizes are locally adap...

This work is devoted to the numerical simulation of a Vlasov-Poisson equation modeling charged particles in a beam submitted to a highly oscillatory external electric field. A numerical scheme is constructed for this model. This scheme is uniformly accurate with respect to the size of the fast time oscillations of the solution, which means that no time step refinement is required to simulate th...

Numerical solution of Richards’ equation remains challenging to get robust, accurate and cost-effective results, particularly for moving sharp wetting fronts. An adaptive strategy both space time is proposed deal with 2D fronts associated varying possibly vanishing diffusivity caused by nonlinearity, heterogeneity anisotropy. Adaptive stepping makes nonlinear convergence reliable backward diffe...